Question

Write each exponential equation in logarithmic form.41.5 = 8

Answer 1

We have the following equation

`4^(1.5)=8`

Using the logarithm of 2 on both sides, we have

`\log _24^(1.5)=\log _28`

We can rewrite the arguments of the both logs

`\begin{gathered} \log _24^(1.5)=\log _28 \\ \log _24^(1.5)=\log _22^3 \end{gathered}`

Using the following property

`\log _ab^c=c\log _a_{}b`

We can rewrite our expression as

`\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}`

And this is a way of rewriting our expression in logarithmic form