What is the answer to 10x^{2log_{10}(x)}=x^3 ?

The answer to 10x^{2log_{10}(x)}=x^3 is x=10,x=sqrt(10)

Solve for x: 10x^{2log_{10}(x)}=x^3

The solution is x=10,x=sqrt(10)

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10 x^{2 l o g_{10} (x)} = x^{3}

x = 10, x = 10

Decimal Notation

x = 10, x = 3.16227 \dots

Solution steps

10 x^{2 l o g_{10} (x)} = x^{3}

Divide both sides by

10

x^{2 l o g_{10} (x)} = \frac{x ^{3}}{10}

Apply log rules

2 lo g_{10} (x) lo g_{10} (x) = 3 lo g_{10} (x) - 1

Rewrite the equation with

lo g_{10} (x) = u

2 uu = 3 u - 1

Solve

2 uu = 3 u - 1 : u = 1, u = \frac{1}{2}

u = 1, u = \frac{1}{2}

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 1 : x = 10

Solve

lo g_{10} (x) = \frac{1}{2} : x = 10

x = 10, x = 10

Verify Solutions:

x = 10

True

, x = 10

True

The solutions are

x = 10, x = 10

ln (2 x - 1) = 0

lo g_{10} (n) = 4

lo g_{4} (8 x) = 3

lo g_{2} (5 + x) = 2 lo g_{2} (x - 1) + 1

lo g_{10} ((x - 1)^{2}) = 0

What is the answer to 10x^{2log_{10}(x)}=x^3 ?
The answer to 10x^{2log_{10}(x)}=x^3 is x=10,x=sqrt(10)
Solve for x: 10x^{2log_{10}(x)}=x^3
The solution is x=10,x=sqrt(10)