Algebra Examples

$\log_{11} (121)$

Step 1

Rewrite as an equation.

$\log_{11} (121) = x$

Step 2

Rewrite $\log_{11} (121) = x$ 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 $b^{y} = x$ .

$11^{x} = 121$

Step 3

Create equivalent expressions in the equation that all have equal bases.

$11^{x} = 11^{2}$

Step 4

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

$x = 2$

Step 5

The variable $x$ is equal to $2$ .

$2$