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

Solution:

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,

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