What is the answer to 4^x+4^{2x}=272 ?

The answer to 4^x+4^{2x}=272 is x=2

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4^x+4^{2x}=272

4^{x} + 4^{2 x} = 272

x = 2

Solution steps

4^{x} + 4^{2 x} = 272

Apply exponent rules

4^{x} + (4^{x})^{2} = 272

Rewrite the equation with

4^{x} = u

u + (u)^{2} = 272

Solve

u + u^{2} = 272 : u = 16, u = - 17

u = 16, u = - 17

Substitute back

u = 4^{x},

solve for

x

Solve

4^{x} = 16 : x = 2

Solve

4^{x} = - 17 :

No Solution for

x \in R

x = 2

3 - 2^{x} = - 5

\frac{a ^{x} + 1}{a ^{x}} = n

2^{\frac{2}{( l o g _{5} ( x ) )}} = \frac{1}{16}

x, (d^{3} + 2 d^{2} - d - 2) = e^{x}

\frac{( 3 2 ^{x - 4} )}{( 4 ^{x - 4} )} = 8^{3 x + 2}