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

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

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

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

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

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

Decimal Notation

x = - 3.41902 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

x 3^{(- 3 x - 8)} = 3^{(- 6 x + 3)}

9^{3 x - 4} = 8 1^{2 x - 5}

2^{x} = 1080

2 = (1.025)^{x}

8 1^{y} 3^{- \frac{2 y}{3}} = 243

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