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

The answer to 2^{3x-2}=3^{2x+1} is x=(ln(12))/(3ln(2)-2ln(3))

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

The solution is x=(ln(12))/(3ln(2)-2ln(3))

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

x = \frac{ln ( 12 )}{3 ln ( 2 ) - 2 ln ( 3 )}

Decimal Notation

x = - 21.09732 \dots

Solution steps

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

Apply exponent rules

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

Solve

(3 x - 2) ln (2) = (2 x + 1) ln (3) : x = \frac{ln ( 12 )}{3 ln ( 2 ) - 2 ln ( 3 )}

x = \frac{ln ( 12 )}{3 ln ( 2 ) - 2 ln ( 3 )}

6^{2 x} - 6^{x} - 30 = 0

2. 5^{x - 3} = 6.25

(e^{5})^{3 x} = e^{5} e^{3 x}

5^{2 x - 16} = 2 5^{3 x + 2}

4^{x^{2}} \cdot 2^{5 x} = 8

What is the answer to 2^{3x-2}=3^{2x+1} ?
The answer to 2^{3x-2}=3^{2x+1} is x=(ln(12))/(3ln(2)-2ln(3))
Solve for x: 2^{3x-2}=3^{2x+1}
The solution is x=(ln(12))/(3ln(2)-2ln(3))