What is the answer to 3^{2x-1}-2^x=0 ?

The answer to 3^{2x-1}-2^x=0 is x=(ln(3))/(2ln(3)-ln(2))

Solve for x: 3^{2x-1}-2^x=0

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

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3^{2 x - 1} - 2^{x} = 0

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

Decimal Notation

x = 0.73042 \dots

Solution steps

3^{2 x - 1} - 2^{x} = 0

Add

2^{x}

to both sides

3^{2 x - 1} - 2^{x} + 2^{x} = 0 + 2^{x}

Simplify

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

Apply exponent rules

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

Solve

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

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

144 \cdot 2^{\frac{x}{3}} = 16

2^{3 x - 1} = 8^{x + 2}

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

75 \cdot 3^{x} = 375

9^{x} - 12 \times 3^{x} + 27 = 0

What is the answer to 3^{2x-1}-2^x=0 ?
The answer to 3^{2x-1}-2^x=0 is x=(ln(3))/(2ln(3)-ln(2))
Solve for x: 3^{2x-1}-2^x=0
The solution is x=(ln(3))/(2ln(3)-ln(2))