Answered

Use the Change of Base Formula to evaluate log3 58. Then convert log3 58 to a logarithm in base 4. Round to the nearest thousandth.

Verified Answer :

caylus

Hello,

\(log_3(58)= \dfrac{ln(58)}{ln(3)}=3,69597450... \\ log_3(58)=log_4(x)\\ \dfrac{ln(58)}{ln(3)} = \dfrac{ln(x)}{4}==\textgreater\ x=e^{ \frac{ln(58)*ln(4)}{ln(3)}}\\ =167,957104437222249066099...\)

≈167.96

isyllus

Answer:

\(\log_358\approx 3.696\)

\(\Rightarrow \dfrac{\log_458}{\log_43}\)

Step-by-step explanation:

Given: \(\log_358\)

We need to re-write the log expression with base 4 using base change property of log.

Log property:

\(\log_ab=\dfrac{\log_cb}{\log_ca}\)

Evaluate:

\(\Rightarrow \log_358\)

\(\Rightarrow \dfrac{\log58}{\log3}\)

\(\Rightarrow \dfrac{1.763427}{0.47712}\approx 3.696\)

Convert with base 4:

\(\Rightarrow \log_358\)

\(\Rightarrow \dfrac{\log_458}{\log_43}\)

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