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

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

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

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

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

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

Decimal Notation

x = - 4.30132 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

8^{3 x + 2} = 1 6^{x - 4}

(625)^{x} = 125

95 = 2 3^{x}

2^{x} + 3^{x} = 0

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