Answer
The value of x is $9$ .
Work Step by Step
Consider the logarithmic equation.
${{\log }_{x}}81=2$ …… (1)
The function ${{\log }_{x}}81=2$ is in the form of $m={{\log }_{a}}p$,where$m=2,a=x\text{ and }p=81$.
Then, the function ${{\log }_{x}}81=2$ can be rewrite as,
${{x}^{2}}=81$
Apply square root property.
$\begin{align}
& x=\pm \sqrt{81} \\
& =\pm 9
\end{align}$
Therefore, the value of x is $9$ and $-9$.
Check:
Substitute $x=9$ in equation (1).
$\begin{align}
{{\log }_{9}}81\overset{?}{\mathop{=}}\,2 & \\
{{\log }_{9}}{{9}^{2}}\overset{?}{\mathop{=}}\,2 & \\
2=2 & \\
\end{align}$
It is true.
Substitute $x=-9$ in equation (1).
${{\log }_{-9}}81\overset{?}{\mathop{=}}\,2$
The log is not defined for a negative base.
It is false.
