Precalculus Examples

{log}_{3} (59049)

$\log_{3} (59049)$

Step 1

Rewrite as an equation.

$\log_{3} (59049) = x$

Step 2

Rewrite

$\log_{3} (59049) = x$ 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

$b^{y} = x$ .

$3^{x} = 59049$

Step 3

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

$3^{x} = 3^{10}$

Step 4

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

$x = 10$

Step 5

The variable

$x$ is equal to

$10$ .

$10$