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

The answer to 2^{1/2 (x+2)}=3^{x-1} is x=(2ln(6))/(2ln(3)-ln(2))

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

The solution is x=(2ln(6))/(2ln(3)-ln(2))

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

x = \frac{2 ln ( 6 )}{2 ln ( 3 ) - ln ( 2 )}

Decimal Notation

x = 2.38253 \dots

Solution steps

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

Apply exponent rules

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

Solve

\frac{1}{2} (x + 2) ln (2) = (x - 1) ln (3) : x = \frac{2 ln ( 6 )}{2 ln ( 3 ) - ln ( 2 )}

x = \frac{2 ln ( 6 )}{2 ln ( 3 ) - ln ( 2 )}

2^{x^{2} - 2 x} = 8

e^{x^{2}} = 0

4^{x} = 10 - 4^{x + 1}

3^{2 x - 1} = 27

e^{2 x} = 9

What is the answer to 2^{1/2 (x+2)}=3^{x-1} ?
The answer to 2^{1/2 (x+2)}=3^{x-1} is x=(2ln(6))/(2ln(3)-ln(2))
Solve for x: 2^{1/2 (x+2)}=3^{x-1}
The solution is x=(2ln(6))/(2ln(3)-ln(2))