Evaluate log base 9 of 27

$\log_{9} (27)$

Rewrite as an equation.

$\log_{9} (27) = x$

Rewrite $\log_{9} (27) = x$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ does not equal $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$9^{x} = 27$

Create expressions in the equation that all have equal bases.

${(3^{2})}^{x} = 3^{3}$

Rewrite ${(3^{2})}^{x}$ as $3^{2 x}$ .

$3^{2 x} = 3^{3}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 x = 3$

Solve for $x$ .

$x = \frac{3}{2}$

The variable $x$ is equal to $\frac{3}{2}$ .

$\frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$

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