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

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

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

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

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

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

Decimal Notation

x = - 8.21439 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

2^{n} + 2^{n} = 2^{n + 1}

5 \cdot 2^{x} + 2^{x + 2} = 18

x, e^{x} = \frac{y}{y - 2}

8^{2 x - 1} = \frac{1}{2 ^{x - 5}}

3^{2 x - 8} = 5^{2 x - 8}

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