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

Question

asked Oct 3, 2023 135k views

1 Answer

Reker · Answer 1 · 2023-10-09T16:33:53+0000

Solution:

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

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