Algebra Examples

$\log_{9} (\frac{1}{729})$

Step 1

Rewrite as an equation.

$\log_{9} (\frac{1}{729}) = x$

Step 2

Rewrite $\log_{9} (\frac{1}{729}) = x$ 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 $b^{y} = x$ .

$9^{x} = \frac{1}{729}$

Step 3

Create expressions in the equation that all have equal bases.

${(3^{2})}^{x} = 3^{- 6}$

Step 4

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

$3^{2 x} = 3^{- 6}$

Step 5

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

$2 x = - 6$

Step 6

Solve for $x$ .

$x = - 3$

Step 7

The variable $x$ is equal to $- 3$ .

$- 3$