Question

solve for x.
\log_{x} 81 = 2
simplify your answer as much as possible.
x =

Explanation:

Step1: Recall the logarithmic definition

The logarithmic equation $\log_{x} 81 = 2$ can be converted to its exponential form using the definition of a logarithm: if $\log_{a} b = c$, then $a^{c}=b$. So we have $x^{2}=81$.

Step2: Solve for x

To solve for $x$, we take the square root of both sides. Remember that for $x^{2}=81$, $x = \pm\sqrt{81}$, but since the base of a logarithm must be positive and not equal to 1, we discard the negative solution. So $x=\sqrt{81}=9$.

Answer:

$x = 9$