What is the answer to 2^{2x+11}=3^{x-5} ?

The answer to 2^{2x+11}=3^{x-5} is x=(-5ln(3)-11ln(2))/(2ln(2)-ln(3))

Solve for x: 2^{2x+11}=3^{x-5}

The solution is x=(-5ln(3)-11ln(2))/(2ln(2)-ln(3))

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2^{2 x + 11} = 3^{x - 5}

x = \frac{- 5 ln ( 3 ) - 11 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

Decimal Notation

x = - 45.59783 \dots

Solution steps

2^{2 x + 11} = 3^{x - 5}

Apply exponent rules

(2 x + 11) ln (2) = (x - 5) ln (3)

Solve

(2 x + 11) ln (2) = (x - 5) ln (3) : x = \frac{- 5 ln ( 3 ) - 11 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

x = \frac{- 5 ln ( 3 ) - 11 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

(\frac{2}{5})^{x} = \frac{4}{25}

(x - 6)^{x^{2} - 5} = (x - 6)^{2 x + 3}

2^{3 x} = 8^{2 x + 1}

(\frac{1}{100})^{2 x} = 0.0001

3^{2 x - 3} = \frac{2 7 ^{x + 1}}{2}

What is the answer to 2^{2x+11}=3^{x-5} ?
The answer to 2^{2x+11}=3^{x-5} is x=(-5ln(3)-11ln(2))/(2ln(2)-ln(3))
Solve for x: 2^{2x+11}=3^{x-5}
The solution is x=(-5ln(3)-11ln(2))/(2ln(2)-ln(3))