What is the answer to 5^{2x+2}=3^{5x-1} ?

The answer to 5^{2x+2}=3^{5x-1} is x=(ln(75))/(5ln(3)-2ln(5))

Solve for x: 5^{2x+2}=3^{5x-1}

The solution is x=(ln(75))/(5ln(3)-2ln(5))

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5^{2 x + 2} = 3^{5 x - 1}

x = \frac{ln ( 75 )}{5 ln ( 3 ) - 2 ln ( 5 )}

Decimal Notation

x = 1.89847 \dots

Solution steps

5^{2 x + 2} = 3^{5 x - 1}

Apply exponent rules

(2 x + 2) ln (5) = (5 x - 1) ln (3)

Solve

(2 x + 2) ln (5) = (5 x - 1) ln (3) : x = \frac{ln ( 75 )}{5 ln ( 3 ) - 2 ln ( 5 )}

x = \frac{ln ( 75 )}{5 ln ( 3 ) - 2 ln ( 5 )}

\frac{( 8 \cdot 2 ^{n} + 2 \cdot 2 ^{n} )}{( - 2 ^{n + 1} + 4 \cdot 2 ^{n} )} = 5^{n}

e^{x} - 3 x = 0

4^{x} + 4^{x} + 2^{x} = 1

3^{x + 4} = 9^{x + 13}

x, 8^{2 x} \cdot 3^{- \frac{1}{2} \cdot y} = 36

What is the answer to 5^{2x+2}=3^{5x-1} ?
The answer to 5^{2x+2}=3^{5x-1} is x=(ln(75))/(5ln(3)-2ln(5))
Solve for x: 5^{2x+2}=3^{5x-1}
The solution is x=(ln(75))/(5ln(3)-2ln(5))