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

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

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

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

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

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

Decimal Notation

x = 0.64095 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

49 (7^{2 x}) - 344 (7^{x}) + 7 = 0

1 6^{m - 1} = 4^{m + 1}

2^{2 x} - 3 \cdot 2^{x} + 2 = 0

150 = 350 - 335 e^{15 k}

2^{5 x + 15} = 1 6^{3 x + 1}

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