Sure, let's solve the equation [tex]\(\log_4 (8x) = 3\)[/tex] step by step.
1. Rewrite the logarithmic equation in its exponential form.
Logarithmic form: [tex]\(\log_4 (8x) = 3\)[/tex]
Exponential form: [tex]\(4^3 = 8x\)[/tex]
2. Calculate [tex]\(4^3\)[/tex].
We know that:
[tex]\[
4^3 = 4 \times 4 \times 4 = 64
\][/tex]
3. Set up the equation with [tex]\(8x\)[/tex].
So, we have:
[tex]\[
64 = 8x
\][/tex]
4. Solve for [tex]\(x\)[/tex].
To isolate [tex]\(x\)[/tex], divide both sides of the equation by 8:
[tex]\[
x = \frac{64}{8}
\][/tex]
5. Simplify the fraction.
[tex]\[
\frac{64}{8} = 8
\][/tex]
Therefore, the solution to the equation [tex]\(\log_4 (8x) = 3\)[/tex] is:
[tex]\[
x = 8
\][/tex]
So, the correct answer from the given options is:
[tex]\[
x = 8
\][/tex]
