Algebra Examples

{log}_{6} (216)

$\log_{6} (216)$

Step 1

Rewrite as an equation.

{log}_{6} (216) = x

$\log_{6} (216) = x$

Step 2

Rewrite

{log}_{6} (216) = x

$\log_{6} (216) = x$ in exponential form using the definition of a logarithm. If

x

$x$ and

b

$b$ are positive real numbers and

b

$b$ does not equal

1

$1$ , then

{log}_{b} (x) = y

$\log_{b} (x) = y$ is equivalent to

b^{y} = x

$b^{y} = x$ .

6^{x} = 216

$6^{x} = 216$

Step 3

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

6^{x} = 6^{3}

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

Step 4

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

x = 3

$x = 3$

Step 5

The variable

x

$x$ is equal to

3

$3$ .

3

$3$