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    • ▾Algebra 2
      • ▸Polynomial arithmetic
        • •Descartes's rule of signs
        • •Difficult factoring problems
        • •Polynomial long division and graphing cubics
        • •Rational root theorem
        • •Higher-order polynomials
        • •Remainder theorem
        • •Factor theorem
        • •Sum and difference of cubes
        • •Reciprocal polynomials
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        • •Multiplying binomials by polynomials
        • •Proving the sum and difference of cubes formulas
        • •Factoring and solving polynomials by graphing
      • ▸Complex numbers
        • •Intro to complex numbers
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        • •Dividing complex numbers
        • •Modulus and argument of a complex number
        • •Proving properties of the complex modulus
        • •Converting complex numbers between polar and rectangular form
        • •Powers of complex numbers using modulus and argument
        • •Square root of a complex number
        • •Distance and midpoint of complex numbers
        • •Linear factorization
        • •Solving equations with complex numbers
        • •Quadratic equations with complex solutions
        • •Complex conjugate root theorem
        • •Fundamental theorem of algebra
      • ▸Polynomial factorization, division, and end behavior
        • •Finding the GCD and LCM of polynomials
        • •Sophie Germain's identity
        • •Dividing a polynomial by a monomial
        • •Dividing quadratics by linear expressions
        • •Polynomial long division
        • •Synthetic division
        • •Converting improper algebraic fractions to mixed algebraic fractions
      • ▸Rational exponents and radicals
        • •Adding and subtracting radicals
        • •Converting between radicals and rational exponents
        • •Rewrite exponential expressions
        • •Simplifying expressions with radicals and rational exponents
        • •Solving equations with radicals and rational exponents
        • •Transformations of the square and cube root functions
      • ▾Logarithms
        • •Evaluating logarithms
        • •Evaluating natural logarithms
        • •Converting between logarithmic form and exponential form
        • •Evaluating logarithmic expressions using the one-to-one property
        • ▾Expanding and condensing logarithmic expressions
          • •Expanding logarithmic expressions
          • ▾Condensing logarithmic expressions
            • •Lesson
            • •Practice
        • •Inverses of exponential and logarithmic functions
        • ▸Graphing logarithmic functions
          • •Sketching logarithmic functions under transformations
        • ▸Basic properties of logarithms
          • •Intro
          • •Proofs
          • •Using the theorems
        • •Change of base formula
        • •Properties of logarithms cheat sheet
        • •Solving logarithmic inequalities
        • •Solving literal equations using properties of logarithms
        • ▸Solving logarithmic equations
          • •Solving logarithmic equations using the one-to-one property
          • •Solving logarithmic equations using the properties of logarithms
        • •Verifying logarithmic identities
        • •Fractal dimension
        • •Logarithmic scale
        • •Approximating logarithms
      • ▸Transformations of functions
        • •Shifting, scaling, and reflecting
        • •Even and odd functions
        • •Wishful thinking strategy
      • ▸Equations and inequalities
        • •Solving literal equations
        • •Alternative quadratic formula
        • ▸Solving exponential equations
          • ▸Solving exponential equations using the one-to-one property
            • •Lesson
            • •Practice
        • •Intersections of lines, circles, and parabolas
        • •Solving and graphing polynomial inequalities using a sign chart
        • •Solving and graphing rational inequalities using a sign chart
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      • ▸Rational functions
        • •Adding and subtracting rational expressions
        • •Finding the domain and range of rational functions
        • •Graphing rational functions
        • •Asymptotes and intercepts of rational functions
        • •Graphing reciprocal functions
        • •Multiplying and dividing rational expressions
        • •Simplifying complex fractions with variables
        • •Simplifying rational expressions
        • •Simplifying square roots of rational expressions
        • •Solving literal rational equations
        • •Solving rational equations
     › Algebra 2 › Logarithms › Expanding and condensing logarithmic expressions › Condensing logarithmic expressions

    Condensing logarithmic expressions: Practice

    Condense:  \(\ln 5 + 5\ln 3\)
    $$\begin{align} & \ln 5 + 5\ln 3 \\ & \ln 5 + \ln 3^5 \\ & \ln\left(5 \cdot 3^5\right) \\ & \ln 1215 \end{align}$$
    \(\dfrac{1}{3}\ln(x + 2)^3 + \dfrac{1}{2}\left[\ln x - \ln\left(x^2 + 3x + 2\right)^2\right]
    \(\ln \dfrac{\sqrt{x}}{x + 1}\)
    72367Express the quantity as a single logarithm. 1/3 ln(x+2)^3 + 1/2[ln x- ln(x^2+ 3x +2)^2]
    Ms Shaws Math Class
    Condense:  \(\ln 3 + \dfrac{1}{3}\ln 8\)
    $$\begin{align} & \ln 3 + \dfrac{1}{3}\ln 8 \\ & \ln 3 + \ln 8^{1 / 3} \\ & \ln 3 + \ln 2 \\ & \ln\left(3 \cdot 2\right) \\ & \ln 6 \end{align}$$
    Condense:  \(\log_5 7 + \log_5 3x\)
    $$\begin{align} & \log_5 7 + \log_5 3x \\ =\ & \log_5(7 \cdot 3x) \\ =\ & \log_5 21x \end{align}$$
    14124Learn basics for learning to CONDENSING a logarithmic expression
    Brian McLogan
    Condense:  \(\log_4 20 + \log_4 3\)
    $$\begin{align} & \log_4 20 + \log_4 3 \\ =\ & \log_4(20 \cdot 3) \\ =\ & \log_4(60) \end{align}$$
    Condense:  \(\log_2 18 - \log_2 3\)
    $$\begin{align} & \log_2 18 - \log_2 3 \\ =\ & \log_2 \dfrac{18}{3} \\ =\ & \log_2 6 \end{align}$$
    Condense:  \(2\log x + 3\log y + 4\log z\)
    $$\begin{align} & 2\log x + 3\log y + 4\log z \\ =\ & \log x^2 + \log y^3 + \log z^4 \\ =\ & \log x^2y^3z^4 \end{align}$$
    Condense:  \(\log_3 2 - 4\log_3 x\)
    $$\begin{align} & \log_3 2 - 4\log_3 x \\[0.5em] =\ & \log_3 2 - \log_3 x^4 \\[0.5em] =\ & \log_3 \dfrac{2}{x^4} \end{align}$$
    13014Learn how to condense a two logarithmic expressions separated by subtraction
    Brian McLogan
    Condense:  \(2\ln 5 - \ln 3\)
    $$\begin{align} & 2\ln 5 - \ln 3 \\ =\ & \ln 5^2 - \ln 3 \\ =\ & \ln 25 - \ln 3 \\ =\ & \ln \dfrac{25}{3} \end{align}$$
    20084Learn how to condense natural logs separated by subtraction
    Brian McLogan
    Condense:  \(\dfrac{1}{4}[\log_2(x - 1) + \log_2(x + 1) - 3\log_2 x]\)
    13361Learn to condense logarithmic expressions to one single logarithm
    Brian McLogan
    Condense:  \(2\log_3 x - 3\left[\log_3(x - 1) + 5\log z\right]\)
    23043How to rewrite a logarithmic expression as one single logarithm
    Brian McLogan
    Condense:  \(2\log_3 x - 3\left[\log_3(x - 1) + 5\log z\right]\)
    23043How to rewrite a logarithmic expression as one single logarithm
    Brian McLogan
    Condense:  \(\ln x - 4[\ln(x - 2) + \ln(x + 2)]\)
    17172Condensing logarithms with multiple parentheses
    Brian McLogan
    Condense:  \(\ln - 4[\ln(x + 2) + \ln(x - 2)]\)
    12413Condensing mulitple logarithms
    Brian McLogan
    Condense:  \((\log 3 - \log 4) - \log 2\)
    22019Condensing a logarithmic expression and simplifying the expression
    Brian McLogan
    Condense:  \(\dfrac{1}{3}\left[2\ln(x + 5) - \ln x - \ln\left(x^2 - 4\right)\right]\)
    15025Simplifying a logarithmic expression by condensing multiple terms
    Brian McLogan
    Condense:  \(\dfrac{1}{2}\left[\log_4(x + 1) + 2\log_4(x - 1)\right] + 6\log_4 x\)
    18354Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(\log_5 y - 4(\log_5 r + 2\log_5 t)\)
    21897How to condense a log expression with parenthesis
    Brian McLogan
    Condense:  \(\dfrac{1}{3}\left[2\ln(x + 3) + \ln x - \ln\left(x^2 - 1\right)\right]\)
    23297Condensing a large logarithmic expression to one single logarithm
    Brian McLogan
    Condense:  \(\dfrac{1}{3}\left[2\ln(x + 3) + \ln x - \ln\left(x^2 - 1\right)\right]\)
    19843Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(\dfrac{1}{2}[3\log_2 x - 2\log_2 z]\)
    19415Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(2[3\ln x - \ln(x + 1) - \ln(x - 1)]\)
    13622Condensing a logarithmic expression to one logarithm
    Brian McLogan
    Condense:  \((\log 3 - \log 4) - \log 2\)
    18317Condensing a logarithmic expression with parenthesis
    Brian McLogan
    Condense:  \(\dfrac{1}{3}(\log_2 x - \log_2 y)\)
    13505How to condense a logarithmic expression using a radical
    Brian McLogan
    Condense:  \(\dfrac{1}{3}\log_4 27 - \left(2\log_4 6 - \dfrac{1}{2}\log_4 81\right)\)
    14857Learn how to condense a logarithmic expression with multiple logs
    Brian McLogan
    Condense:  \(\log_5 y - 4(\log_5 r + 2\log_5 t)\)
    16919Condensing logarithmic expressions with three logs
    Brian McLogan
    Condense:  \(\dfrac{1}{3}\log_6 8 + 2\log_6 x + 3\log_6 y\)
    13242How to condense a logarithmic expression with three logs
    Brian McLogan
    Condense:  \(\dfrac{1}{3}\log 3x + \dfrac{2}{3}\log 3x\)
    13857Condensing a logarithmic expression with fractions
    Brian McLogan
    Condense:  \(\log_3 x + 2\log_3 x + 3\log_3 x\)
    20325The easy way to condensing logarithmic expressions
    Brian McLogan
    Condense:  \(\log_2 3 + \log_2 4 - 2\log_2 x\)
    19257Condense a logarithmic expression with product and quotient
    Brian McLogan
    Condense:  \(\log_{10} x - 2\log_{10} y + 3\log_{10} z\)
    16280Using the properties of logarithms to condense multiple logarithms
    Brian McLogan
    Condense:  \(4\log_3 x + \dfrac{1}{2}\log_3(x - 2) + \log_3 x^2\)
    17978Properties of logarithms for condensing an expression
    Brian McLogan
    Condense:  \(\ln(2x - 4) + \ln(3x + 2) + \ln 2\)
    20535Condensing a logarithmic expression into one single quantity using the product rule
    Brian McLogan
    Condense:  \(3\ln\left(x^3y\right) + 2\ln\left(yz^2\right)\)
    14230Condense a natural logarithmic expression
    Brian McLogan
    Condense:  \(\log_5 6 - \log_5 4\)
    19675Learn how to condense a logarithm over subtraction of two logs
    Brian McLogan
    Condense:  \(2\log x + 3\log y\)
    22277Learning the basics for condensing logarithmic expressions
    Brian McLogan
    Condense:  \(2[3\log x + \log(x - 1)]\)
    20868Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(2\log x - 3\log y\)
    22093Condensing a logarithmic expression
    Brian McLogan
    Condense:  \(3\ln x - 4\ln 5z - \dfrac{1}{4}\ln y\)
    19929Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(\log_8 x + \log_8 10\)
    22917Condensing a basic logarithmic expression
    Brian McLogan
    Condense:  \(2\log_2(x + 3)\)
    20516Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(\log_4 x + \log_4 y\)
    14220Condensing logarithmic expression into one single expression
    Brian McLogan
    Condense:  \(\log_{10} x - \log_{10} 3\)
    14667Learn how to condense the difference of two logarithmic expressions
    Brian McLogan
    Condense:  \(3\log x - \log 5\)
    22176Rewriting a logarithmic expression as one logarithm by condensing
    Brian McLogan
    Condense:  \(6\ln x + 4\ln y\)
    21337Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(\log_3 x + 2\log_3 x - \log_3 27\)
    21832Learn how to condense logarithmic expression to one log
    Brian McLogan
    Condense:  \(3\log_3 x + 4\log_3 y - 4\log_3 z\)
    12377Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(3\log x + \dfrac{1}{3}\log y\)
    18743Learn the steps to condense a logarithmic expression
    Brian McLogan
    Condense:  \(\dfrac{1}{4}\log_3 5x\)
    18369Rewriting a logarithmic equation with a fraction in front
    Brian McLogan
    Condense:  \(\log_5 3x\)
    19127Learn the basics for expanding and condensing a logarithmic equation
    Brian McLogan
    Condense:  \(\dfrac{1}{4}\log_3 5x\)
    21657How to use the properties of logs to condense an expression
    Brian McLogan
    Condense:  \(\log_{10} x - 2\log_{10} y + 3\log_{10} z\)
    21657How to use the properties of logs to condense an expression
    Brian McLogan
    Condense:  \(\dfrac{1}{5}\log_3 x\)
    16159Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(\ln(x^2 - 3) - 2\ln x - \ln(x + 1)\)
    16551Simplifying a logarithmic expression to one single logarithm
    Brian McLogan
    Condense:  \(\log x + \log(x^2 - 4) - \log 15 - \log(x + 2)\)
    13486Simplifying multiple logarithms into one single quantity
    Brian McLogan
    Condense:  \(\log_2 x + 2\log_2 y - \log_2 4\)
    14997Learn the basics for condensing a logarithmic expression with addition and subtraction
    Brian McLogan
    Condense:  \(6\log_8 2 + 2\log_8 x + 2\log_8 y\)
    13172Condensing a logarithmic expression using power and product property
    Brian McLogan
    Condense:  \(3\log_2 x + 3\log_2 x + 2\log_2 y\)
    22342Learning the basics for condensing a logarithmic expression
    Brian McLogan
    Condense:  \(\ln 40 + 2\ln \dfrac{1}{2} + \ln x\)
    12995Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(3\log_4 x + \log_4 z - \log_4 3\)
    21078Using multiple properties to help us condense an expression with three logs
    Brian McLogan
    Condense:  \(2\log_{10} x + \log_{10} 5\)
    14477Math tutorial for condensing a logarithmic expression with two logs
    Brian McLogan
    Condense:  \(\ln x + \ln 3\)
    20589Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(\log_4 7 - \log_4 10\)
    12957Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(-4\log_8 2x + \log_8(x + 1)\)
    20155Condensing logarithmic expressions
    Brian McLogan
    Condense:  \(8\log_2 x + \dfrac{1}{2}\log_2 y - 3\log_2 z\)
    69910Write a Log Expression as a Single Log: 8log_8 x +1/2log_8 y-3log_8 z
    Prof. Redden

    YouTube videos

    • 17402Summary for condensing logarithmic expressions
      Brian McLogan
    • 17925What do I need to know to condense logarithmic expressions
      Brian McLogan
    • 12444How to condense logarithmic expressions
      Brian McLogan
    • 2046Condensing Logarithmic Expressions
      The Organic Chemistry Tutor