What is the answer to 2*x^{1+log_{2}(x)}=x^3 ?

The answer to 2*x^{1+log_{2}(x)}=x^3 is x=2

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2*x^{1+log_{2}(x)}=x^3

2 \cdot x^{1 + l o g_{2} (x)} = x^{3}

x = 2

Solution steps

2 x^{1 + l o g_{2} (x)} = x^{3}

Divide both sides by

2

x^{1 + l o g_{2} (x)} = \frac{x ^{3}}{2}

Apply log rules

(1 + lo g_{2} (x)) lo g_{2} (x) = 3 lo g_{2} (x) - 1

Rewrite the equation with

lo g_{2} (x) = u

(1 + u) u = 3 u - 1

Solve

(1 + u) u = 3 u - 1 : u = 1

u = 1

Substitute back

u = lo g_{2} (x),

solve for

x

Solve

lo g_{2} (x) = 1 : x = 2

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

x, e^{2} = ln (x)

- 2 = ln ∣ x ∣

ln (x + 8) + ln (10) = 3

x, f x = ln (14 x)

25 - ln (3 - x) = 0

What is the answer to 2*x^{1+log_{2}(x)}=x^3 ?
The answer to 2*x^{1+log_{2}(x)}=x^3 is x=2
Solve for x: 2*x^{1+log_{2}(x)}=x^3
The solution is x=2