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

The answer to 3^{x-1}=2^{x+3} is x=(ln(24))/(ln(3)-ln(2))

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

The solution is x=(ln(24))/(ln(3)-ln(2))

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

x = \frac{ln ( 24 )}{ln ( 3 ) - ln ( 2 )}

Decimal Notation

x = 7.83804 \dots

Solution steps

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

Apply exponent rules

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

Solve

(x - 1) ln (3) = (x + 3) ln (2) : x = \frac{ln ( 24 )}{ln ( 3 ) - ln ( 2 )}

x = \frac{ln ( 24 )}{ln ( 3 ) - ln ( 2 )}

e^{2 x} - 2 e^{x + 1} + e^{2} = 0

4^{- x} = \frac{1}{64}

2^{2 x + 3} + 2^{x + 3} = 2^{0} + 2^{x}

2^{x + 3} = 8

e^{x} + x - 3 = 0

What is the answer to 3^{x-1}=2^{x+3} ?
The answer to 3^{x-1}=2^{x+3} is x=(ln(24))/(ln(3)-ln(2))
Solve for x: 3^{x-1}=2^{x+3}
The solution is x=(ln(24))/(ln(3)-ln(2))