Question

Use the properties of logarithms to expand logyz2.Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.

Answer 1

Given:

`log(yz^2)`

Applying the property of logarithm;

`log(AB)=logA+logB`

Hence,

`log(yz^2)=log\text{ }y+log\text{ }z^2`

Also, applying the property of logarithm:

`log\text{ }a^x=xlog\text{ }a`

Hence,

`log\text{ }y+log\text{ }z^2=log\text{ }y+2logz`

Therefore,

`log(yz^2)=log\text{ }y+2log\text{ }z`