What is the answer to 2^x+2^{3x}=10 ?

The answer to 2^x+2^{3x}=10 is x=1

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2^x+2^{3x}=10

2^{x} + 2^{3 x} = 10

x = 1

Solution steps

2^{x} + 2^{3 x} = 10

Apply exponent rules

2^{x} + (2^{x})^{3} = 10

Rewrite the equation with

2^{x} = u

u + (u)^{3} = 10

Solve

u + u^{3} = 10 : u = 2

u = 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 2 : x = 1

x = 1

y, x = 3^{y}

e^{3 - 4 x} = 4

6 = 2 x + 4^{x}

4^{x} - 4^{x - 1} = 24