Question

What is the exact value of x?

5 ⋅ 8^4x = 376




x=4log75.2/log8

x=4log8/log75.2

x=log75.2/4log8

x=log8/4log75.2

Answer 1

`x=(\log(75.2))/(4\log(8))`

Explanation:

`\begin{aligned}5 \cdot 8^(4x) & =376\\8^(4x) & = (376)/(5)\\8^(4x) & =75.2\end{aligned}`

Taking logs of both sides:

`\implies \log(8)^(4x)=\log(75.2)`

Using the power log rule
`\log_a(x)^n=n\log_a(x)` :

`\implies 4x\log(8)=\log(75.2)`

Solving for x:

`\begin{aligned}\implies 4x\log(8) & =\log(75.2)\\\\ 4x & =(\log(75.2))/(\log(8))\\\\x & =(\log(75.2))/(4\log(8))\\\end{aligned}`