What is the answer to 9^{x-1}=4^{2x} ?

The answer to 9^{x-1}=4^{2x} is x=(ln(3))/(ln(3)-2ln(2))

Solve for x: 9^{x-1}=4^{2x}

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

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

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

Decimal Notation

x = - 3.81884 \dots

Solution steps

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

Apply exponent rules

(x - 1) ln (9) = 2 x ln (4)

Solve

(x - 1) ln (9) = 2 x ln (4) : x = \frac{ln ( 3 )}{ln ( 3 ) - 2 ln ( 2 )}

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

\frac{15}{e ^{2 x}} = 3

3^{2 x + 1} = 27

4^{2 x + 1} = 4

2^{n + 1} = 32

e^{x} - x^{2} = 0

What is the answer to 9^{x-1}=4^{2x} ?
The answer to 9^{x-1}=4^{2x} is x=(ln(3))/(ln(3)-2ln(2))
Solve for x: 9^{x-1}=4^{2x}
The solution is x=(ln(3))/(ln(3)-2ln(2))