Question

solve the equation.
log₅ x² = 2
select the correct choice below and fill in any answer boxes present in your choice.
a. x =
(simplify your answer, including any radicals. use integers or fractions for any numbers in it)
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 $\log_{5}x^{2}=2$, we have $x^{2}=5^{2}$.

Step2: Solve for x

If $x^{2}=25$, then taking the square - root of both sides gives $x=\pm\sqrt{25}$. So $x = 5$ or $x=- 5$.

Answer:

A. $x = 5$ or $x=-5$