Question

solve the equation. give the solution in exact form.\\(\log _{4}(x + 7)(x - 5) = 3\\)\
rewrite the given equation without logarithms. do not solve for \\(x\\).

Explanation:

Step1: Recall logarithm definition

The logarithmic equation $\log_b a = c$ is equivalent to $b^c = a$ (where $b>0, b
eq1, a>0$).

Step2: Apply to given equation

For $\log_4[(x + 7)(x - 5)] = 3$, here $b = 4$, $a=(x + 7)(x - 5)$, $c = 3$.
Using the definition, we rewrite it as $4^3=(x + 7)(x - 5)$.

Answer:

$4^3=(x + 7)(x - 5)$ (or simplified as $64=(x + 7)(x - 5)$)