Trigonometry Examples

$\log_{16} (8)$

Step 1

Rewrite as an equation.

$\log_{16} (8) = x$

Step 2

Rewrite

$\log_{16} (8) = x$ 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

$b^{y} = x$ .

$16^{x} = 8$

Step 3

Create expressions in the equation that all have equal bases.

${(2^{4})}^{x} = 2^{3}$

Step 4

Rewrite

${(2^{4})}^{x}$ as

$2^{4 x}$ .

$2^{4 x} = 2^{3}$

Step 5

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

$4 x = 3$

Step 6

Solve for

$x$ .

$x = \frac{3}{4}$

Step 7

The variable

$x$ is equal to

$\frac{3}{4}$ .

$\frac{3}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$