What is the answer to 4^{x-1}=3^{2x} ?

The answer to 4^{x-1}=3^{2x} is x=(ln(2))/(ln(2)-ln(3))

Solve for x: 4^{x-1}=3^{2x}

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

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4^{x - 1} = 3^{2 x}

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

Decimal Notation

x = - 1.70951 \dots

Solution steps

4^{x - 1} = 3^{2 x}

Apply exponent rules

(x - 1) ln (4) = 2 x ln (3)

Solve

(x - 1) ln (4) = 2 x ln (3) : x = \frac{ln ( 2 )}{ln ( 2 ) - ln ( 3 )}

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

3^{x + 2} + 3^{x + 1} + 3^{x} + 3^{x - 1} = 120

9^{x} - 7 \times 3^{x} - 18 = 0

\frac{8 1 ^{3 n + 2}}{24 3 ^{- n}} = 3^{4}

12 e^{2 x} = 200

2^{x} \times 3^{x} = 81

What is the answer to 4^{x-1}=3^{2x} ?
The answer to 4^{x-1}=3^{2x} is x=(ln(2))/(ln(2)-ln(3))
Solve for x: 4^{x-1}=3^{2x}
The solution is x=(ln(2))/(ln(2)-ln(3))