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Exercise

$3\log\left(x\right)-2\log\left(2y\right)$

Step-by-step Solution

1

Apply the formula: $a\log_{b}\left(x\right)$$=\log_{b}\left(x^a\right)$

$\log \left(x^3\right)-2\log \left(2y\right)$
2

Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$

$\log \left(x^3\right)-\log \left(\left(2y\right)^{2}\right)$
3

The difference of two logarithms of equal base $b$ is equal to the logarithm of the quotient: $\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)$

$\log \left(\frac{x^3}{\left(2y\right)^{2}}\right)$

Final answer to the exercise

$\log \left(\frac{x^3}{\left(2y\right)^{2}}\right)$

Try other ways to solve this exercise

  • Choose an option
  • Condense the logarithm
  • Expand the logarithm
  • Simplify
  • Find the integral
  • Find the derivative
  • Write as single logarithm
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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Similar Questions Solved

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$\log\left(\frac{1}{2}\right)\cdot 32$

$\log_3\left(b\right)+\log_3\left(b+2\right)$

Main Topic: Condensing Logarithms

Combining or condensing logarithms consists of rewriting a mathematical expression with several logarithms into a single logarithm, by applying the properties of logarithms.

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