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

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

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

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

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

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

Decimal Notation

x = - 5.37384 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

7^{3 - x} = 5^{x + 1}

4^{x + 5} - 4^{x + 4} = 384

3^{1 - x^{2}} = \frac{1}{27}

e^{x} = - 2

2^{x} - 1 = x + 2

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