Question

Which logarithmic graph can be used to approximate the value of y in the equation 4^y=8

Answer 1

$\bf \textit{exponential form of a logarithm}\\\\ log_{{ a}}{{ b}}=y \implies {{ a}}^y={{ b}}\qquad\qquad % exponential notation 2nd form {{ a}}^y={{ b}}\implies log_{{ a}}{{ b}}=y \\\\ -------------------------------$

$\bf 4^y=8\implies log_4(8)=y\qquad \begin{cases} 4=2^2\\ 8=2^3 \end{cases}\implies (2^2)^y=2^3 \\\\\\ 2^{2y}=2^3\impliedby \textit{since the bases are the same, so are the exponents} \\\\\\ 2y=3\implies y=\cfrac{3}{2}\implies y=1\frac{1}{2}\quad thus\quad \begin{cases} x=8\\ y=\frac{3}{2} \end{cases}$

so.. check your graphs