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

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

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

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

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

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

Decimal Notation

x = 5.41902 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

(\frac{1}{5})^{x} = 10

e^{x} = 24

e^{x} = 23

e^{x} = 35

3 (2)^{x} = 42

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