Solve for x (5^(4x+3))/(25^(9-x))=5^(2x+5)

$\frac{5^{4 x + 3}}{25^{9 - x}} = 5^{2 x + 5}$

Move $25^{9 - x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$5^{4 x + 3} \cdot 25^{- (9 - x)} = 5^{2 x + 5}$

Rewrite $25$ as $5^{2}$ .

$5^{4 x + 3} \cdot {(5^{2})}^{- (9 - x)} = 5^{2 x + 5}$

Multiply the exponents in ${(5^{2})}^{- (9 - x)}$ .

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

$5^{4 x + 3} \cdot 5^{2 (- (9 - x))} = 5^{2 x + 5}$

Apply the distributive property.

$5^{4 x + 3} \cdot 5^{2 (- 1 \cdot 9 - - x)} = 5^{2 x + 5}$

Multiply $- 1$ by $9$ .

$5^{4 x + 3} \cdot 5^{2 (- 9 - - x)} = 5^{2 x + 5}$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$5^{4 x + 3} \cdot 5^{2 (- 9 + 1 x)} = 5^{2 x + 5}$

Multiply $x$ by $1$ .

$5^{4 x + 3} \cdot 5^{2 (- 9 + x)} = 5^{2 x + 5}$

Apply the distributive property.

$5^{4 x + 3} \cdot 5^{2 \cdot - 9 + 2 x} = 5^{2 x + 5}$

Multiply $2$ by $- 9$ .

$5^{4 x + 3} \cdot 5^{- 18 + 2 x} = 5^{2 x + 5}$

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

$5^{4 x + 3 - 18 + 2 x} = 5^{2 x + 5}$

Add $4 x$ and $2 x$ .

$5^{6 x + 3 - 18} = 5^{2 x + 5}$

Subtract $18$ from $3$ .

$5^{6 x - 15} = 5^{2 x + 5}$

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

$6 x - 15 = 2 x + 5$

Solve for $x$ .

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

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

$6 x - 15 - 2 x = 5$

Subtract $2 x$ from $6 x$ .

$4 x - 15 = 5$

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

Add $15$ to both sides of the equation.

$4 x = 5 + 15$

Add $5$ and $15$ .

$4 x = 20$

Divide each term in $4 x = 20$ by $4$ and simplify.

Divide each term in $4 x = 20$ by $4$ .

$\frac{4 x}{4} = \frac{20}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{20}{4}$

Divide $x$ by $1$ .

$x = \frac{20}{4}$

Simplify the right side.

Divide $20$ by $4$ .

$x = 5$

Solve for x (5^(4x+3))/(25^(9-x))=5^(2x+5)

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