Solve for x log base 9 of x=5/2

$\log_{9} (x) = \frac{5}{2}$

Rewrite $\log_{9} (x) = \frac{5}{2}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ $\neq$ $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$9^{\frac{5}{2}} = x$

Solve for $x$

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Simplify the expression.

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Rewrite $9$ as $3^{2}$ .

${(3^{2})}^{\frac{5}{2}} = x$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{2 (\frac{5}{2})} = x$

Cancel the common factor of $2$ .

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Cancel the common factor.

$3^{2 (\frac{5}{2})} = x$

Rewrite the expression.

$3^{5} = x$

Raise $3$ to the power of $5$ .

$243 = x$

Rewrite the equation as $x = 243$ .

$x = 243$

Solve for x log base 9 of x=5/2

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