Question

Use the change of base formula to compute log/174.Round your answer to the nearest thousandth.

Answer 1

The Expression is given below as

`\log_{(1)/(7)}4`

Represent the expression above to be

`=x`

That is, we will have that

`\log_{(1)/(7)}4=x`

Applying the change of base rule below, we will have that

`\begin{gathered} \log_ab=y \\ b=a^y \\ lnb=lna^y \\ lnb=ylna \\ y=(lnb)/(lna) \end{gathered}`
`\begin{gathered} \log_{(1)/(7)}4=x \\ ((1)/(7))^x=4 \\ (7^(-1))^x=4 \\ 7^(-x)=4 \\ take\text{ ln of both sides} \\ ln7^(-x)=ln4 \\ -xln7=ln4 \\ dividie\text{ both sides by -ln7} \\ (-xln7)/(-ln7)=(ln4)/(-ln7) \\ x=-0.712 \end{gathered}`

Hence,

The final answer is

`\rightarrow-0.712`