Question

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.

Answer 1

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

Answer 2

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:

$\Rightarrow \log_358$

$\Rightarrow \dfrac{\log_458}{\log_43}$