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

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

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

The solution is x=10,x= 1/(10^{2/3)}

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

x = 10, x = \frac{1}{1 0 ^{\frac{2}{3}}}

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{10} (x) = u

3 uu = u + 2

Solve

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

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

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

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

Solve

lo g_{10} (x) = - \frac{2}{3} : x = \frac{1}{1 0 ^{\frac{2}{3}}}

x = 10, x = \frac{1}{1 0 ^{\frac{2}{3}}}

Verify Solutions:

x = 10

True

, x = \frac{1}{1 0 ^{\frac{2}{3}}}

True

The solutions are

x = 10, x = \frac{1}{1 0 ^{\frac{2}{3}}}

ln (x^{4}) = 6

2 lo g_{10} (x) = 4 lo g_{10} (3)

x, y = ln (x^{2} + y^{2})

lo g_{5} (x) + lo g_{5} (4 x - 1) = 1

ln (x) - ln (3) = 4

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