What is the answer to 6*2^{x^2-2x+2}=4*3^{x^2-2x+2} ?

The answer to 6*2^{x^2-2x+2}=4*3^{x^2-2x+2} is x=-(-2ln(2)+2ln(3))/(2(ln(2)-ln(3)))

Solve for x: 6*2^{x^2-2x+2}=4*3^{x^2-2x+2}

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

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6 \cdot 2^{x^{2} - 2 x + 2} = 4 \cdot 3^{x^{2} - 2 x + 2}

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

Decimal Notation

x = 1

Solution steps

6 \cdot 2^{x^{2} - 2 x + 2} = 4 \cdot 3^{x^{2} - 2 x + 2}

Apply exponent rules

ln (6) + (x^{2} - 2 x + 2) ln (2) = ln (4) + (x^{2} - 2 x + 2) ln (3)

Solve

ln (6) + (x^{2} - 2 x + 2) ln (2) = ln (4) + (x^{2} - 2 x + 2) ln (3) : x = - \frac{- 2 ln ( 2 ) + 2 ln ( 3 )}{2 ( ln ( 2 ) - ln ( 3 ) )}

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

2^{x - 1} + 2^{x - 2} + 2^{x - 3} + 2^{x - 4} = 960

6^{x - 7} - 8 = 40

1 1^{x + 6} = 3^{x}

4 x e^{x} = 2

What is the answer to 6*2^{x^2-2x+2}=4*3^{x^2-2x+2} ?
The answer to 6*2^{x^2-2x+2}=4*3^{x^2-2x+2} is x=-(-2ln(2)+2ln(3))/(2(ln(2)-ln(3)))
Solve for x: 6*2^{x^2-2x+2}=4*3^{x^2-2x+2}
The solution is x=-(-2ln(2)+2ln(3))/(2(ln(2)-ln(3)))