Precalculus Examples

$8^{x} = 32$

Step 1

Subtract $32$ from both sides of the equation.

$8^{x} - 32 = 0$

Step 2

Add $32$ to both sides of the equation.

$8^{x} = 32$

Step 3

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

$2^{3 x} = 2^{5}$

Step 4

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

$3 x = 5$

Step 5

Divide each term in $3 x = 5$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{3}$