Precalculus Examples

$2^{x} = 8 (2^{- x})$

Step 1

Rewrite $8$ as $2^{3}$ .

$2^{x} = 2^{3} \cdot 2^{- x}$

Step 2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3

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

$x = 3 - x$

Step 4

Solve for $x$ .

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Step 4.1

Move all terms containing $x$ to the left side of the equation.

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Step 4.1.1

Add $x$ to both sides of the equation.

$x + x = 3$

Step 4.1.2

Add $x$ and $x$ .

$2 x = 3$

Step 4.2

Divide each term in $2 x = 3$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 x = 3$ by $2$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $x$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

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