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

How do I evaluate each of these logarithms, use exact values and show my work for-example-1
User Raulp
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1 Answer

18 votes
18 votes

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

User Earl
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