Answer:
[tex]x=\dfrac{\log(75.2)}{4\log(8)}[/tex]
Step-by-step explanation:
[tex]\begin{aligned}5 \cdot 8^{4x} & =376\\8^{4x} & = \dfrac{376}{5}\\8^{4x} & =75.2\end{aligned}[/tex]
Taking logs of both sides:
[tex]\implies \log(8)^{4x}=\log(75.2)[/tex]
Using the power log rule [tex]\log_a(x)^n=n\log_a(x)[/tex] :
[tex]\implies 4x\log(8)=\log(75.2)[/tex]
Solving for x:
[tex]\begin{aligned}\implies 4x\log(8) & =\log(75.2)\\\\ 4x & =\dfrac{\log(75.2)}{\log(8)}\\\\x & =\dfrac{\log(75.2)}{4\log(8)}\\\end{aligned}[/tex]
