Question

How do I evaluate each of these logarithms, use exact values and show my work for these problems?

Answer 1

The equation is given below as

`\begin{gathered} \log_2x=-5 \\ \log_ab=y \\ b=a^y \end{gathered}`

By applying the law above, we will have

`\begin{gathered} \log_2x=-5 \\ x=2^(-5) \\ x=(1)/(2^5) \\ x=(1)/(32) \end{gathered}`

Hence,

The final answer is

`\Rightarrow x=(1)/(32)`

Part B:

The expression is given below as

`\begin{gathered} \log_4((1)/(64)) \\ \log_4(64^(-1)) \\ \log_4(4^(-3)) \\ -3\log_44 \\ =-3*1 \\ =-3 \end{gathered}`

Hence,

The final answer is

`\Rightarrow\log_4((1)/(64))=-3`