Algebra Examples

8^{x} = 16

$8^{x} = 16$

Step 1

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

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

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

Step 2

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

3 x = 4

$3 x = 4$

Step 3

Divide each term in

3 x = 4

$3 x = 4$ by

3

$3$ and simplify.

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Step 3.1

Divide each term in

3 x = 4

$3 x = 4$ by

3

$3$ .

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

3

$3$ .

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Step 3.2.1.1

Cancel the common factor.

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

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

Step 3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{4}{3}

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

x = \frac{4}{3}

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

x = \frac{4}{3}

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

x = \frac{4}{3}

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

Step 4

The result can be shown in multiple forms.

Exact Form:

x = \frac{4}{3}

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

Decimal Form:

x = 1.\overline{3}

$x = 1.\overline{3}$

Mixed Number Form:

x = 1 \frac{1}{3}

$x = 1 \frac{1}{3}$

8^{x} = 16

$8^{x} = 16$

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