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Exercise

$\log_{3\sqrt[3]{3}}$

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 $M=3^{0.5}$ and $N=3$

$\log_{3}\left(3^{0.5}\right)+\log_{3}\left(3\right)$
2

Evaluating the logarithm of base $3$ of $3$

$\log_{3}\left(3^{0.5}\right)+1$
3

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

$0.5+1$
4

Add the values $0.5$ and $1$

$1.5$

Final answer to the exercise

$1.5$

Try other ways to solve this exercise

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  • Integrate by partial fractions
  • Product of Binomials with Common Term
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