we have the functions
[tex]\begin{gathered} f(x)=5logx \\ g(x)=logx^5 \end{gathered}[/tex]
Find out (g/f)(x)
[tex]\left(g/f\right)\left(x\right)=\frac{g(x)}{f(x)}=\frac{logx^5}{5logx}[/tex]
Apply property of logarithms
[tex]\begin{gathered} (\frac{g}{f})(x)=\frac{logx^{5}}{5logx}=\frac{5logx}{5logx}=1 \\ \\ therefore \\ \\ (\frac{g}{f})(x)=1 \end{gathered}[/tex]
The answer is 1
