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

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

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x^{log_{10}(x)}=100x

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

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

Decimal

x = 100, x = 0.1

Solution steps

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

Apply log rules

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

Rewrite the equation with

lo g_{10} (x) = u

uu = u + 2

Solve

uu = u + 2 : u = 2, u = - 1

u = 2, u = - 1

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

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

Solve

lo g_{10} (x) = - 1 : 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_{a} (x)

lo g_{10} (x + 5) = 1.2

lo g_{10} (x) = lo g_{10} (36) - 9

lo g_{10} (x^{2}) + lo g_{10} (25) = 2

2 ln (x) - ln (2 x - 3) = ln (5 x) - ln (x + 2)

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