What is the answer to 2^{2x+6}=3^{x-9} ?

The answer to 2^{2x+6}=3^{x-9} is x=(-9ln(3)-6ln(2))/(2ln(2)-ln(3))

Solve for x: 2^{2x+6}=3^{x-9}

The solution is x=(-9ln(3)-6ln(2))/(2ln(2)-ln(3))

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2^{2 x + 6} = 3^{x - 9}

x = \frac{- 9 ln ( 3 ) - 6 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

Decimal Notation

x = - 48.82610 \dots

Solution steps

2^{2 x + 6} = 3^{x - 9}

Apply exponent rules

(2 x + 6) ln (2) = (x - 9) ln (3)

Solve

(2 x + 6) ln (2) = (x - 9) ln (3) : x = \frac{- 9 ln ( 3 ) - 6 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

x = \frac{- 9 ln ( 3 ) - 6 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

36 (6^{2 x}) + 179 (6^{x}) - 5 = 0

30000 = 3000 e^{k \cdot 10}

1 6^{x} + 4^{x + 1} - 3 = 0

\frac{k ( x )}{2 ^{x}} = 0

1 0^{y} = 0

What is the answer to 2^{2x+6}=3^{x-9} ?
The answer to 2^{2x+6}=3^{x-9} is x=(-9ln(3)-6ln(2))/(2ln(2)-ln(3))
Solve for x: 2^{2x+6}=3^{x-9}
The solution is x=(-9ln(3)-6ln(2))/(2ln(2)-ln(3))