Precalculus Examples

$9^{4 x} = 3^{x + 4}$

Step 1

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

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

Step 2

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

$2 (4 x) = x + 4$

Step 3

Solve for $x$ .

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Step 3.1

Multiply $4$ by $2$ .

$8 x = x + 4$

Step 3.2

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

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Step 3.2.1

Subtract $x$ from both sides of the equation.

$8 x - x = 4$

Step 3.2.2

Subtract $x$ from $8 x$ .

$7 x = 4$

Step 3.3

Divide each term in $7 x = 4$ by $7$ and simplify.

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Step 3.3.1

Divide each term in $7 x = 4$ by $7$ .

$\frac{7 x}{7} = \frac{4}{7}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $7$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{4}{7}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{7}$

Decimal Form:

$x = 0.\overline{571428}$