What is the answer to 2(2^{2x})+4=9(2^x) ?

The answer to 2(2^{2x})+4=9(2^x) is x=2,x=-1

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2(2^{2x})+4=9(2^x)

2 (2^{2 x}) + 4 = 9 (2^{x})

x = 2, x = - 1

Solution steps

2 (2^{2 x}) + 4 = 9 (2^{x})

Apply exponent rules

(2^{x})^{2} \cdot 2^{1} + 4 = 9 \cdot 2^{x}

Rewrite the equation with

2^{x} = u

(u)^{2} \cdot 2^{1} + 4 = 9 u

Solve

u^{2} \cdot 2^{1} + 4 = 9 u : u = 4, u = \frac{1}{2}

u = 4, u = \frac{1}{2}

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 4 : x = 2

Solve

2^{x} = \frac{1}{2} : x = - 1

x = 2, x = - 1

\frac{40}{1 + e ^{- x}} = 2

e^{x} - 2 e^{- x} - 1 = 0

1 1^{x - 8} - 11 = 48

2 = e^{5 x}

1 0^{x} = 5 \cdot 1 0^{- x}

What is the answer to 2(2^{2x})+4=9(2^x) ?
The answer to 2(2^{2x})+4=9(2^x) is x=2,x=-1
Solve for x: 2(2^{2x})+4=9(2^x)
The solution is x=2,x=-1