Question

Expand each logarithm. log₄5 x

Answer 1

If the expression is log₄5 x,then the expansion of this will look like

(log 5+ log x)/log 4.

Given that the expression is log₄5 x.

We are required to find the expansion of the expression.

Base change theorem says that $log_{a}b$=$log_{x}b/log_{x}a$. We use the change of base formula to re-write a logarithm operation as a fraction of logarithms with a new base.

The expression is log₄5 x.

log₄5 x=(log 5+log x)/log 4

(We know that $log_{a}b$= log b/ log a and log mn =log m +log n)

Hence if the expression is log₄5 x then the expansion of this will look like (log 5+ log x)/log 4.

Learn more about base change theorem at brainly.com/question/14998693

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