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

The answer to 5^{2x+3}=3^{x-1} is x=-(ln(375))/(2ln(5)-ln(3))

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

The solution is x=-(ln(375))/(2ln(5)-ln(3))

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

x = - \frac{ln ( 375 )}{2 ln ( 5 ) - ln ( 3 )}

Decimal Notation

x = - 2.79537 \dots

Solution steps

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

Apply exponent rules

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

Solve

(2 x + 3) ln (5) = (x - 1) ln (3) : x = - \frac{ln ( 375 )}{2 ln ( 5 ) - ln ( 3 )}

x = - \frac{ln ( 375 )}{2 ln ( 5 ) - ln ( 3 )}

e^{2 x} - e^{x} - 110 = 0

3 (3 e^{- x} x^{2} - e^{- x} x^{3}) = 0

3 2^{2 x + 4} = 1 6^{2 x + 4}

8 1^{2 x + 1} = 9^{5 x - 1}

2 \times 4^{x} = 2

What is the answer to 5^{2x+3}=3^{x-1} ?
The answer to 5^{2x+3}=3^{x-1} is x=-(ln(375))/(2ln(5)-ln(3))
Solve for x: 5^{2x+3}=3^{x-1}
The solution is x=-(ln(375))/(2ln(5)-ln(3))