What is the answer to x^{2log_{10}(x)}=100x^3 ?

The answer to x^{2log_{10}(x)}=100x^3 is x=100,x= 1/(sqrt(10))

Solve for x: x^{2log_{10}(x)}=100x^3

The solution is x=100,x= 1/(sqrt(10))

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x^{2 l o g_{10} (x)} = 100 x^{3}

x = 100, x = \frac{1}{10}

Decimal

x = 100, x = 0.31622 \dots

Solution steps

x^{2 l o g_{10} (x)} = 100 x^{3}

Apply log rules

2 lo g_{10} (x) lo g_{10} (x) = 3 lo g_{10} (x) + 2

Rewrite the equation with

lo g_{10} (x) = u

2 uu = 3 u + 2

Solve

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

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

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 2 : x = 100

Solve

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

x = 100, x = \frac{1}{10}

Verify Solutions:

x = 100

True

, x = \frac{1}{10}

True

The solutions are

x = 100, x = \frac{1}{10}

lo g_{10} (2 x + 4) = 2

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

lo g_{32} (x) = \frac{6}{5}

lo g_{7} (x) = 1.6

x, ln (x y^{3}) = x y

What is the answer to x^{2log_{10}(x)}=100x^3 ?
The answer to x^{2log_{10}(x)}=100x^3 is x=100,x= 1/(sqrt(10))
Solve for x: x^{2log_{10}(x)}=100x^3
The solution is x=100,x= 1/(sqrt(10))