Question

solve the equation.
log₈ x² = 2
select the correct choice below and fill in any answer
a. x =
(simplify your answer, including any radicals.
b. there is no solution.

Explanation:

Step1: Convert to exponential form

By the definition of logarithms, if $\log_{a}b = c$, then $b=a^{c}$. So for $\log_{8}x^{2}=2$, we have $x^{2}=8^{2}$.

Step2: Calculate $8^{2}$

$8^{2}=64$, so the equation becomes $x^{2}=64$.

Step3: Solve for $x$

Taking the square - root of both sides, we get $x=\pm\sqrt{64}=\pm8$.

Answer:

A. $x = \pm8$