We have the following equation
[tex]4^{1.5}=8[/tex]Using the logarithm of 2 on both sides, we have
[tex]\log _24^{1.5}=\log _28[/tex]We can rewrite the arguments of the both logs
[tex]\begin{gathered} \log _24^{1.5}=\log _28 \\ \log _24^{1.5}=\log _22^3 \end{gathered}[/tex]Using the following property
[tex]\log _ab^c=c\log _a_{}b[/tex]We can rewrite our expression as
[tex]\begin{gathered} \log _24^{1.5}=\log _22^3 \\ \log _24^{1.5}=3\log _22 \\ \log _24^{1.5}=3 \\ 1.5\log _24^{}=3 \\ \log _24^{}=2 \end{gathered}[/tex]And this is a way of rewriting our expression in logarithmic form
