Solve for x (1/16)^(3x+5)=(1/64)^(x+4)

${(\frac{1}{16})}^{3 x + 5} = {(\frac{1}{64})}^{x + 4}$

Step 1

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

${(\frac{1}{4})}^{2 (3 x + 5)} = {(\frac{1}{4})}^{3 (x + 4)}$

Step 2

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

$2 (3 x + 5) = 3 (x + 4)$

Step 3

Solve for $x$ .

Simplify $2 (3 x + 5)$ .

Start simplifying.

$0 + 0 + 2 (3 x + 5) = 3 (x + 4)$

Simplify by adding zeros.

$2 (3 x + 5) = 3 (x + 4)$

Apply the distributive property.

$2 (3 x) + 2 \cdot 5 = 3 (x + 4)$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 \cdot 5 = 3 (x + 4)$

Multiply $2$ by $5$ .

$6 x + 10 = 3 (x + 4)$

Simplify $3 (x + 4)$ .

Apply the distributive property.

$6 x + 10 = 3 x + 3 \cdot 4$

Multiply $3$ by $4$ .

$6 x + 10 = 3 x + 12$

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

Subtract $3 x$ from both sides of the equation.

$6 x + 10 - 3 x = 12$

Subtract $3 x$ from $6 x$ .

$3 x + 10 = 12$

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

Subtract $10$ from both sides of the equation.

$3 x = 12 - 10$

Subtract $10$ from $12$ .

$3 x = 2$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.\overline{6}$

Solve for x (1/16)^(3x+5)=(1/64)^(x+4)

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