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scoray [572]
3 years ago
15

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

th.
Mathematics
2 answers:
boyakko [2]3 years ago
6 0

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}

Natali5045456 [20]3 years ago
5 0
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
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