What is the answer to 2^{2x+7}=3^{x-4} ?

The answer to 2^{2x+7}=3^{x-4} is x=(-4ln(3)-7ln(2))/(2ln(2)-ln(3))

Solve for x: 2^{2x+7}=3^{x-4}

The solution is x=(-4ln(3)-7ln(2))/(2ln(2)-ln(3))

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2^{2 x + 7} = 3^{x - 4}

x = \frac{- 4 ln ( 3 ) - 7 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

Decimal Notation

x = - 32.14131 \dots

Solution steps

2^{2 x + 7} = 3^{x - 4}

Apply exponent rules

(2 x + 7) ln (2) = (x - 4) ln (3)

Solve

(2 x + 7) ln (2) = (x - 4) ln (3) : x = \frac{- 4 ln ( 3 ) - 7 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

x = \frac{- 4 ln ( 3 ) - 7 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

2^{n - 1} = 360000

6 \cdot e^{x} = 25

e^{5 - 4 x} = 6

e^{5 - 4 x} = 7

500 = 2000 \cdot (2^{- 0.1 x})

What is the answer to 2^{2x+7}=3^{x-4} ?
The answer to 2^{2x+7}=3^{x-4} is x=(-4ln(3)-7ln(2))/(2ln(2)-ln(3))
Solve for x: 2^{2x+7}=3^{x-4}
The solution is x=(-4ln(3)-7ln(2))/(2ln(2)-ln(3))