Given:
a logarithm is given as
[tex]log(z^5x)[/tex]
Find:
we have to expand the given logarithm expressionusing properties of logarithm.
Explanation:
we know from the properties of logarithm that
[tex]\begin{gathered} log(m^n)=nlog(m) \\ and \\ log(mn)=log(m)+log(n) \end{gathered}[/tex]
we will use above properties to expand the given logarithm expression as follows
[tex]log(z^5x)=logz^5+logx=5logz+logx[/tex]
Therefore, the expansion of the given logarithm is 5 log(z)+ log(x)
