What is the answer to 3^{2x+1}=5^{3x-2} ?

The answer to 3^{2x+1}=5^{3x-2} is x=(ln(75))/(3ln(5)-2ln(3))

Solve for x: 3^{2x+1}=5^{3x-2}

The solution is x=(ln(75))/(3ln(5)-2ln(3))

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3^{2 x + 1} = 5^{3 x - 2}

x = \frac{ln ( 75 )}{3 ln ( 5 ) - 2 ln ( 3 )}

Decimal Notation

x = 1.64095 \dots

Solution steps

3^{2 x + 1} = 5^{3 x - 2}

Apply exponent rules

(2 x + 1) ln (3) = (3 x - 2) ln (5)

Solve

(2 x + 1) ln (3) = (3 x - 2) ln (5) : x = \frac{ln ( 75 )}{3 ln ( 5 ) - 2 ln ( 3 )}

x = \frac{ln ( 75 )}{3 ln ( 5 ) - 2 ln ( 3 )}

a, (x^{a})^{b} = x^{ab}

1 6^{x} - 12 \cdot 4^{x} + 32 = 0

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

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

What is the answer to 3^{2x+1}=5^{3x-2} ?
The answer to 3^{2x+1}=5^{3x-2} is x=(ln(75))/(3ln(5)-2ln(3))
Solve for x: 3^{2x+1}=5^{3x-2}
The solution is x=(ln(75))/(3ln(5)-2ln(3))