Question

solve. simplify your answer(s). if there are multiple answers, separate them with commas. \\(\log_{8} 5v = \log_{8} (4v + 8)\\) \\(v = \square\\)

Explanation:

Step1: Use Logarithm Property

If \(\log_{a}x=\log_{a}y\), then \(x = y\) (for \(a>0,a
eq1,x>0,y>0\)). Here \(a = 8\), \(x = 5v\), \(y=4v + 8\). So we get \(5v=4v + 8\).

Step2: Solve for \(v\)

Subtract \(4v\) from both sides: \(5v-4v=4v + 8-4v\), which simplifies to \(v = 8\).
We should also check the domain: for \(\log_{8}5v\) and \(\log_{8}(4v + 8)\), when \(v = 8\), \(5v=40>0\) and \(4v + 8=40>0\), so it is valid.

Answer:

\(8\)