Solve for x (8^(2x+4))/(4^(x-3))=4^(x+5)

$\frac{8^{2 x + 4}}{4^{x - 3}} = 4^{x + 5}$

Move $4^{x - 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$8^{2 x + 4} \cdot 4^{- (x - 3)} = 4^{x + 5}$

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

${(2^{3})}^{2 x + 4} \cdot 4^{- (x - 3)} = 4^{x + 5}$

Multiply the exponents in ${(2^{3})}^{2 x + 4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2^{3 (2 x + 4)} \cdot 4^{- (x - 3)} = 4^{x + 5}$

Apply the distributive property.

$2^{3 (2 x) + 3 \cdot 4} \cdot 4^{- (x - 3)} = 4^{x + 5}$

Multiply $2$ by $3$ .

$2^{6 x + 3 \cdot 4} \cdot 4^{- (x - 3)} = 4^{x + 5}$

Multiply $3$ by $4$ .

$2^{6 x + 12} \cdot 4^{- (x - 3)} = 4^{x + 5}$

Rewrite $4$ as $2^{2}$ .

$2^{6 x + 12} \cdot {(2^{2})}^{- (x - 3)} = 4^{x + 5}$

Multiply the exponents in ${(2^{2})}^{- (x - 3)}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2^{6 x + 12} \cdot 2^{2 (- (x - 3))} = 4^{x + 5}$

Apply the distributive property.

$2^{6 x + 12} \cdot 2^{2 (- x - - 3)} = 4^{x + 5}$

Multiply $- 1$ by $- 3$ .

$2^{6 x + 12} \cdot 2^{2 (- x + 3)} = 4^{x + 5}$

Apply the distributive property.

$2^{6 x + 12} \cdot 2^{2 (- x) + 2 \cdot 3} = 4^{x + 5}$

Multiply $- 1$ by $2$ .

$2^{6 x + 12} \cdot 2^{- 2 x + 2 \cdot 3} = 4^{x + 5}$

Multiply $2$ by $3$ .

$2^{6 x + 12} \cdot 2^{- 2 x + 6} = 4^{x + 5}$

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

$2^{6 x + 12 - 2 x + 6} = 4^{x + 5}$

Subtract $2 x$ from $6 x$ .

$2^{4 x + 12 + 6} = 4^{x + 5}$

Add $12$ and $6$ .

$2^{4 x + 18} = 4^{x + 5}$

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

$2^{4 x + 18} = 2^{2 (x + 5)}$

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

$4 x + 18 = 2 (x + 5)$

Solve for $x$ .

Simplify $2 (x + 5)$ .

Rewrite.

$4 x + 18 = 0 + 0 + 2 (x + 5)$

Simplify by adding zeros.

$4 x + 18 = 2 (x + 5)$

Apply the distributive property.

$4 x + 18 = 2 x + 2 \cdot 5$

Multiply $2$ by $5$ .

$4 x + 18 = 2 x + 10$

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

Subtract $2 x$ from both sides of the equation.

$4 x + 18 - 2 x = 10$

Subtract $2 x$ from $4 x$ .

$2 x + 18 = 10$

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

Subtract $18$ from both sides of the equation.

$2 x = 10 - 18$

Subtract $18$ from $10$ .

$2 x = - 8$

Divide each term in $2 x = - 8$ by $2$ and simplify.

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$x = - 4$

Solve for x (8^(2x+4))/(4^(x-3))=4^(x+5)

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