Algebra Examples

{log}_{16} (8)

$\log_{16} (8)$

Step 1

Rewrite as an equation.

{log}_{16} (8) = x

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

Step 2

Rewrite

{log}_{16} (8) = x

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

$b^{y} = x$ .

16^{x} = 8

$16^{x} = 8$

Step 3

Create expressions in the equation that all have equal bases.

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

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

Step 4

Rewrite

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

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

2^{4 x}

$2^{4 x}$ .

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

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

Step 5

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

4 x = 3

$4 x = 3$

Step 6

Solve for

x

$x$ .

x = \frac{3}{4}

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

Step 7

The variable

x

$x$ is equal to

\frac{3}{4}

$\frac{3}{4}$ .

\frac{3}{4}

$\frac{3}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{3}{4}

$\frac{3}{4}$

Decimal Form:

0.75

$0.75$