en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(1/x e^{-y/x})

Solution

simplify

ln (\frac{1}{x} e^{- \frac{y}{x}})

Solution

- \frac{y}{x} - ln (x)

Solution steps

ln (\frac{1}{x} e^{- \frac{y}{x}})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (\frac{1}{x} e^{- \frac{y}{x}}) = ln (\frac{1}{x}) + ln (e^{- \frac{y}{x}})

= ln (\frac{1}{x}) + ln (e^{- \frac{y}{x}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{- \frac{y}{x}}) = - \frac{y}{x} ln (e)

= ln (\frac{1}{x}) - \frac{y}{x} ln (e)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{x}) = ln (1) - ln (x)

= ln (1) - ln (x) - ln (e) \frac{y}{x}

ln (1) = 0

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

= 0 - ln (x) - \frac{y}{x}

0 - ln (x) - \frac{y}{x} = - ln (x) - \frac{y}{x}

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

Popular Examples

simplify ln(47/50)+1/47 simplify

ln (\frac{47}{50}) + \frac{1}{47}

simplify 2ln(2)+ln(10)simplify

2 ln (2) + ln (10)

simplify ln((1-sqrt(2))/(1+sqrt(2)))simplify

ln (\frac{1 - 2}{1 + 2})

simplify 4[ln(x)-ln(x+9)-ln(x-9)]simplify

4 [ln (x) - ln (x + 9) - ln (x - 9)]

simplify ln(((x-2)^5)/((x+1)^3))simplify

ln (\frac{( x - 2 ) ^{5}}{( x + 1 ) ^{3}})

Frequently Asked Questions (FAQ)

What is ln(1/x e^{-y/x}) ?
The solution to ln(1/x e^{-y/x}) is -y/x-ln(x)