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

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

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

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

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

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

Decimal Notation

x = 0.92822 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

5^{4 x - 1} = 25

r, x^{r} = 0

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

3^{2 x} = - 81

- 5 e^{- 5 x} = 0

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