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

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

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

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

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3^{2 (x - 1)} = 2^{x - 3}

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

Decimal Notation

x = 0.07830 \dots

Solution steps

3^{2 (x - 1)} = 2^{x - 3}

Apply exponent rules

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

Solve

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

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

4 e^{2 x} = 7 e^{- 3 x}

51 e^{x} = 510

9^{x + 3} = 24 3^{3 - x}

4 e^{x} = 18

5^{2 x - 1} = 2 (3^{x})

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