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

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

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

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

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

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

Decimal Notation

x = - 0.64095 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

7^{x - 2} - 3^{2 x + 1} = 0

m, n = 2^{m - 1}

3^{x - 6} = 2

1 6^{2 x} = 25 6^{2 x + 5}

3^{2 x + 1} - 18 (3^{x}) - 81 = 0

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