What is the answer to 2^{2x}=2^x+992 ?

The answer to 2^{2x}=2^x+992 is x=5

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2^{2x}=2^x+992

2^{2 x} = 2^{x} + 992

x = 5

Solution steps

2^{2 x} = 2^{x} + 992

Apply exponent rules

(2^{x})^{2} = 2^{x} + 992

Rewrite the equation with

2^{x} = u

(u)^{2} = u + 992

Solve

u^{2} = u + 992 : u = 32, u = - 31

u = 32, u = - 31

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 32 : x = 5

Solve

2^{x} = - 31 :

No Solution for

x \in R

x = 5

e^{7 y} = 6

7^{x^{2} - 4 x + 6} = 343

a^{2 x} = 3

1 2^{x + 5} = 144

125 = 5^{3 x + 6}