What is the answer to 2^x+4^x=1056 ?

The answer to 2^x+4^x=1056 is x=5

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2^x+4^x=1056

2^{x} + 4^{x} = 1056

x = 5

Solution steps

2^{x} + 4^{x} = 1056

Apply exponent rules

2^{x} + (2^{x})^{2} = 1056

Rewrite the equation with

2^{x} = u

u + (u)^{2} = 1056

Solve

u + u^{2} = 1056 : u = 32, u = - 33

u = 32, u = - 33

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 32 : x = 5

Solve

2^{x} = - 33 :

No Solution for

x \in R

x = 5

2 = (1 + \frac{0.06}{0.5})^{0.5 n}

26 = 220 (0.5)^{\frac{x}{6}}

e^{3 x} = 13.68

x, 4^{x + 5} - 4^{x + 4} = 384

x^{l o g_{3} (x)} - 5 = 76