Solve for x 8=16^(7x+2)

$8 = 16^{7 x + 2}$

Step 1

Rewrite the equation as $16^{7 x + 2} = 8$ .

$16^{7 x + 2} = 8$

Step 2

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

$2^{4 (7 x + 2)} = 2^{3}$

Step 3

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

$4 (7 x + 2) = 3$

Step 4

Solve for $x$ .

Divide each term in $4 (7 x + 2) = 3$ by $4$ and simplify.

Divide each term in $4 (7 x + 2) = 3$ by $4$ .

$\frac{4 (7 x + 2)}{4} = \frac{3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (7 x + 2)}{4} = \frac{3}{4}$

Divide $7 x + 2$ by $1$ .

$7 x + 2 = \frac{3}{4}$

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$7 x = \frac{3}{4} - 2$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$7 x = \frac{3}{4} - 2 \cdot \frac{4}{4}$

Combine $- 2$ and $\frac{4}{4}$ .

$7 x = \frac{3}{4} + \frac{- 2 \cdot 4}{4}$

Combine the numerators over the common denominator.

$7 x = \frac{3 - 2 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 2$ by $4$ .

$7 x = \frac{3 - 8}{4}$

Subtract $8$ from $3$ .

$7 x = \frac{- 5}{4}$

Move the negative in front of the fraction.

$7 x = - \frac{5}{4}$

Divide each term in $7 x = - \frac{5}{4}$ by $7$ and simplify.

Divide each term in $7 x = - \frac{5}{4}$ by $7$ .

$\frac{7 x}{7} = \frac{- \frac{5}{4}}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- \frac{5}{4}}{7}$

Divide $x$ by $1$ .

$x = \frac{- \frac{5}{4}}{7}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{5}{4} \cdot \frac{1}{7}$

Multiply $- \frac{5}{4} \cdot \frac{1}{7}$ .

Multiply $\frac{1}{7}$ by $\frac{5}{4}$ .

$x = - \frac{5}{7 \cdot 4}$

Multiply $7$ by $4$ .

$x = - \frac{5}{28}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{28}$

Decimal Form:

$x = - 0.17857142 \dots$

Solve for x 8=16^(7x+2)

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