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Exercise

$\log_b\left(3b^4\right)$

Step-by-step Solution

1

Use the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$, where $M=b^4$ and $N=3$

$\log_{b}\left(b^4\right)+\log_{b}\left(3\right)$
2

Use the following rule for logarithms: $\log_b(b^k)=k$

$4+\log_{b}\left(3\right)$

Final answer to the exercise

$4+\log_{b}\left(3\right)$

Try other ways to solve this exercise

  • Choose an option
  • Solve for b
  • 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
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$\ln\left(3x\right)$

$\log\left(2x\right)$

Main Topic: Expanding Logarithms

Logarithm expansion consists of applying the properties of logarithms to express a single logarithm in multiple logarithms, usually much simpler.

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