What is the answer to 3^{2x-3}=5^{4x+5} ?

The answer to 3^{2x-3}=5^{4x+5} is x=(5ln(5)+3ln(3))/(2(ln(3)-2ln(5)))

Solve for x: 3^{2x-3}=5^{4x+5}

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

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

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

Decimal Notation

x = - 2.67490 \dots

Solution steps

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

Apply exponent rules

(2 x - 3) ln (3) = (4 x + 5) ln (5)

Solve

(2 x - 3) ln (3) = (4 x + 5) ln (5) : x = \frac{5 ln ( 5 ) + 3 ln ( 3 )}{2 ( ln ( 3 ) - 2 ln ( 5 ) )}

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

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

27 = 3^{5 x} 9^{x^{2}}

e^{x} e^{2} = \frac{e ^{4}}{e ^{x + 1}}

3^{x - 1} = \frac{1}{3}

8^{x} = 45

What is the answer to 3^{2x-3}=5^{4x+5} ?
The answer to 3^{2x-3}=5^{4x+5} is x=(5ln(5)+3ln(3))/(2(ln(3)-2ln(5)))
Solve for x: 3^{2x-3}=5^{4x+5}
The solution is x=(5ln(5)+3ln(3))/(2(ln(3)-2ln(5)))