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

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

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

solve for

x, 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 )}

0.2 = 0.9 9^{x}

25 (10)^{2 t} = 208

6 e^{4 x} - 2 = 3

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

3 \cdot 7^{x} = 10.48

What is the answer to solvefor x,2^{3x-1}=5^{x-2} ?
The answer to solvefor x,2^{3x-1}=5^{x-2} is x=(-2ln(5)+ln(2))/(3ln(2)-ln(5))