en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x=e^{(ln(x))/x}

Solution

x = e^{\frac{l n ( x )}{x}}

Solution

x = 1

Solution steps

x = e^{\frac{l n ( x )}{x}}

Apply log rules

ln (x) = \frac{ln ( x )}{x}

Multiply both sides by

x

ln (x) x = \frac{ln ( x )}{x} x

Simplify

ln (x) x = ln (x)

Move

ln (x)

to the left side

ln (x) x - ln (x) = 0

Factor

ln (x) x - ln (x) : ln (x) (x - 1)

ln (x) (x - 1) = 0

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

ln (x) = 0 or x - 1 = 0

Solve

ln (x) = 0 : x = 1

Solve

x - 1 = 0 : x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

Popular Examples

lo g_{x} (x) = 3

ln (3 x) - 1 = 0

5 = 2 lo g_{10} (x)

log_{2}(12-2^x)=2x

lo g_{2} (12 - 2^{x}) = 2 x

x^{log_{4}(x^9)}=(4x)^{12}

x^{l o g_{4} (x^{9})} = (4 x)^{12}

Frequently Asked Questions (FAQ)

What is the answer to x=e^{(ln(x))/x} ?
The answer to x=e^{(ln(x))/x} is x=1