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

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

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

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

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

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

Decimal Notation

x = - 0.86906 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

x = e^{- x}

6^{x + 1} - 18 \cdot 6^{x - 1} = 108

2^{3 x + 2} = 6

1 0^{x + 2} - 12 = 22

2^{x} = A^{\frac{x}{12}}

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