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

The answer to x^{log_{x}(x)}=100x is No Solution for x\in\mathbb{R}

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

The solution is No Solution for x\in\mathbb{R}

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

No Solution for x \in R

Solution steps

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

Apply log rules

1 \cdot 1 = \frac{ln ( 100 x )}{ln ( x )}

Multiply both sides by

ln (x)

1 \cdot 1 \cdot ln (x) = \frac{ln ( 100 x )}{ln ( x )} ln (x)

Simplify

ln (x) = ln (100 x)

Apply log rules

x = 100 x

Solve

x = 100 x : x = 0

x = 0

Verify Solutions:

x = 0

False

The solution is

No Solution for x \in R

\frac{1}{3} lo g_{10} (x) = 1

ln (x) = - 1.69

lo g_{6} (x) = 1

12 - lo g_{7} (x - 1) = 10

4 lo g_{5} (z) - lo g_{z} (5) = 3

What is the answer to x^{log_{x}(x)}=100x ?
The answer to x^{log_{x}(x)}=100x is No Solution for x\in\mathbb{R}
Solve for x: x^{log_{x}(x)}=100x
The solution is No Solution for x\in\mathbb{R}