What is the answer to 2^x-4^x=-12 ?

The answer to 2^x-4^x=-12 is x=2

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2^x-4^x=-12

2^{x} - 4^{x} = - 12

x = 2

Solution steps

2^{x} - 4^{x} = - 12

Apply exponent rules

2^{x} - (2^{x})^{2} = - 12

Rewrite the equation with

2^{x} = u

u - (u)^{2} = - 12

Solve

u - u^{2} = - 12 : u = - 3, u = 4

u = - 3, u = 4

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = - 3 :

No Solution for

x \in R

Solve

2^{x} = 4 : x = 2

x = 2

\frac{3 ^{n - 2}}{9 ^{1 - n}} = 1

9^{x - 1} = 4^{2 x}

\frac{15}{e ^{2 x}} = 3

3^{2 x + 1} = 27

4^{2 x + 1} = 4