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 Notation

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}

ln (x) = 5.297293, x

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

9.3 = - lo g_{10} (x)

x^{1} + lo g_{10} (x) = 10 x

ln (e x - 9 + 4) = 24

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