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

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

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

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

x = 1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

(u)^{3} + u = 10

Solve

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

u = 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 2 : x = 1

x = 1

16 \cdot 4^{v - 2} - 3 = 61

200 = 1000 - 1000 (0.9)^{t}

2 \cdot 1 1^{x} - 4 = 452

3^{2 x + 1} - 2 7^{x} = 0

\frac{3}{5 ^{x}} = 0.12