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Exercise

$\log_b\left(x\right)+\log_b\left(y\right)-\log_b\left(z\right)$

Step-by-step Solution

1

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

$\log_{b}\left(\frac{x}{z}\right)+\log_{b}\left(y\right)$
2

The sum of two logarithms of the same base is equal to the logarithm of the product of the arguments

$\log_{b}\left(\frac{x}{z}y\right)$
3

Multiplying the fraction by $y$

$\log_{b}\left(\frac{xy}{z}\right)$

Final answer to the exercise

$\log_{b}\left(\frac{xy}{z}\right)$

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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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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