• TOC
  • Courses
  • Blog
  • Twitch
  • Shop
  • Search
    • Courses
    • Blog
    • Subreddit
    • Discord
    • Log in
    • Sign up
    • ▾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
        • •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
        • •Direct variation
        • •Inverse variation
      • ▸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

    1. Condensing logarithmic expressions
    2. Expanding logarithmic expressions
    3. Other resources

    Conclude by giving your students these challenges:

    • Fair and Square by Brilliant
    • 2007 AMC 8, Problem 17
    • 2010 AMC 8, Problem 23
    • All Aboard by Pierce School: Problem / Solution

    Mentally determine what fraction is shaded.

    Answer: \(1/4\)

    TODO: Draw or photograph the figure cut up and rearranged.