# Properties of Logarithms Calculator

## Get detailed solutions to your math problems with our Properties of Logarithms step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

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### Difficult Problems

1

Solved example of properties of logarithms

$\log\sqrt{x\cdot y\cdot z}$
2

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$\frac{1}{3}\log \left(xyz\right)$
3

Use the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$, where $M=x$ and $N=yz$

$\frac{1}{3}\left(\log \left(x\right)+\log \left(yz\right)\right)$
4

Use the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$, where $M=y$ and $N=z$

$\frac{1}{3}\left(\log \left(x\right)+\log \left(y\right)+\log \left(z\right)\right)$
5

Multiply the single term $\frac{1}{3}$ by each term of the polynomial $\left(\log \left(x\right)+\log \left(y\right)+\log \left(z\right)\right)$

$\frac{1}{3}\log \left(x\right)+\frac{1}{3}\log \left(y\right)+\frac{1}{3}\log \left(z\right)$

$\frac{1}{3}\log \left(x\right)+\frac{1}{3}\log \left(y\right)+\frac{1}{3}\log \left(z\right)$