Solve for x 8^(6-4x)+6=22

$8^{6 - 4 x} + 6 = 22$

Step 1

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

Subtract $6$ from both sides of the equation.

$8^{6 - 4 x} = 22 - 6$

Subtract $6$ from $22$ .

$8^{6 - 4 x} = 16$

Step 2

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

$2^{3 (6 - 4 x)} = 2^{4}$

Step 3

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

$3 (6 - 4 x) = 4$

Step 4

Solve for $x$ .

Divide each term in $3 (6 - 4 x) = 4$ by $3$ and simplify.

Divide each term in $3 (6 - 4 x) = 4$ by $3$ .

$\frac{3 (6 - 4 x)}{3} = \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (6 - 4 x)}{3} = \frac{4}{3}$

Divide $6 - 4 x$ by $1$ .

$6 - 4 x = \frac{4}{3}$

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

Subtract $6$ from both sides of the equation.

$- 4 x = \frac{4}{3} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 4 x = \frac{4}{3} - 6 \cdot \frac{3}{3}$

Combine $- 6$ and $\frac{3}{3}$ .

$- 4 x = \frac{4}{3} + \frac{- 6 \cdot 3}{3}$

Combine the numerators over the common denominator.

$- 4 x = \frac{4 - 6 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 6$ by $3$ .

$- 4 x = \frac{4 - 18}{3}$

Subtract $18$ from $4$ .

$- 4 x = \frac{- 14}{3}$

Move the negative in front of the fraction.

$- 4 x = - \frac{14}{3}$

Divide each term in $- 4 x = - \frac{14}{3}$ by $- 4$ and simplify.

Divide each term in $- 4 x = - \frac{14}{3}$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- \frac{14}{3}}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- \frac{14}{3}}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- \frac{14}{3}}{- 4}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{14}{3} \cdot \frac{1}{- 4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{14}{3}$ into the numerator.

$x = \frac{- 14}{3} \cdot \frac{1}{- 4}$

Factor $2$ out of $- 14$ .

$x = \frac{2 (- 7)}{3} \cdot \frac{1}{- 4}$

Factor $2$ out of $- 4$ .

$x = \frac{2 \cdot - 7}{3} \cdot \frac{1}{2 \cdot - 2}$

Cancel the common factor.

$x = \frac{2 \cdot - 7}{3} \cdot \frac{1}{2 \cdot - 2}$

Rewrite the expression.

$x = \frac{- 7}{3} \cdot \frac{1}{- 2}$

Multiply $\frac{- 7}{3}$ by $\frac{1}{- 2}$ .

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

Multiply $3$ by $- 2$ .

$x = \frac{- 7}{- 6}$

Dividing two negative values results in a positive value.

$x = \frac{7}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{6}$

Decimal Form:

$x = 1.1\overline{6}$

Mixed Number Form:

$x = 1 \frac{1}{6}$

Solve for x 8^(6-4x)+6=22

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