Question

O EXPONENTIAL AND LOGARITHMIC FUNCTIONSExpanding a logarithmic expression: Problem type 1

Answer 1

Given:

a logarithm is given as

$log(z^5x)$

Find:

we have to expand the given logarithm expressionusing properties of logarithm.

Explanation:

we know from the properties of logarithm that

$\begin{gathered} log(m^n)=nlog(m) \\ and \\ log(mn)=log(m)+log(n) \end{gathered}$

we will use above properties to expand the given logarithm expression as follows

$log(z^5x)=logz^5+logx=5logz+logx$

Therefore, the expansion of the given logarithm is 5 log(z)+ log(x)