Precalculus Examples

$2^{3 x} = 128$

Step 1

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

$2^{3 x} = 2^{7}$

Step 2

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

$3 x = 7$

Step 3

Divide each term in $3 x = 7$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = 7$ by $3$ .

$\frac{3 x}{3} = \frac{7}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{7}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{3}$

Decimal Form:

$x = 2.\overline{3}$

Mixed Number Form:

$x = 2 \frac{1}{3}$