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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
        • •Adding and subtracting polynomials
        • •Multiplying binomials by polynomials
        • •Proving the sum and difference of cubes formulas
        • •Factoring and solving polynomials by graphing
      • ▸Complex numbers
        • •Intro to complex numbers
        • •Powers of the imaginary unit
        • •Simplifying square roots of negative integers
        • •Plotting complex numbers
        • •Adding and subtracting complex numbers
        • •Multiplying complex numbers
        • •Complex number conjugates
        • •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
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        • •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
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        • •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
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        • •Simplifying complex fractions with variables
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        • •Simplifying square roots of rational expressions
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        • •Solving rational equations
     › Algebra 2 › Logarithms › Expanding and condensing logarithmic expressions

    Expanding logarithmic expressions

    In this section, you will learn how to expand logarithmic expressions. That is, you will translate expressions with one log into expressions with multiple logs. Before attempting this section, you should know all the properties of logarithms.

    1. Lesson
    2. Other resources
    3. Practice