Solve for y log base 9 of y=1/2

$\log_{9} (y) = \frac{1}{2}$

Rewrite $\log_{9} (y) = \frac{1}{2}$ 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 $b^{y} = x$ .

$9^{\frac{1}{2}} = y$

Solve for $y$ .

Rewrite the equation as $y = 9^{\frac{1}{2}}$ .

$y = 9^{\frac{1}{2}}$

Simplify $9^{\frac{1}{2}}$ .

Simplify the expression.

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

$y = {(3^{2})}^{\frac{1}{2}}$

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

$y = 3^{2 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y = 3^{2 (\frac{1}{2})}$

Rewrite the expression.

$y = 3^{1}$

Evaluate the exponent.

$y = 3$

Solve for y log base 9 of y=1/2

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