Question

solve the following logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give the exact answer. \\(\log _{2}(8x + 9)=2\\)
rewrite the given equation without logarithms. do not solve for x.

Explanation:

Step1: Recall logarithm definition

The logarithmic equation $\log_b(a) = c$ can be rewritten in exponential form as $b^c = a$. Here, $b = 2$, $a = 8x + 9$, and $c = 2$.

Step2: Apply the definition

Using the exponential form of the logarithm, we substitute the values into $b^c = a$. So we get $2^2 = 8x + 9$.

Answer:

$2^2 = 8x + 9$ (or simplified as $4 = 8x + 9$)