What is ln((e^{-x/2})/(2sqrt(2pi))) ?

The solution to ln((e^{-x/2})/(2sqrt(2pi))) is -ln(2)+(-x-ln(2pi))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((e^{-x/2})/(2sqrt(2pi)))

simplify

ln (\frac{e ^{- \frac{x}{2}}}{2 2 π})

- ln (2) + \frac{- x - ln ( 2 π )}{2}

Solution steps

ln (\frac{e ^{- \frac{x}{2}}}{2 2 π})

Apply log rule:

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

ln (\frac{e ^{- \frac{x}{2}}}{2 2 π}) = ln (e^{- \frac{x}{2}}) - ln (2 2 π)

= ln (e^{- \frac{x}{2}}) - ln (2 2 π)

Apply log rule:

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

ln (e^{- \frac{x}{2}}) = - \frac{x}{2} ln (e)

= - \frac{x}{2} ln (e) - ln (2 2 π)

Apply log rule:

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

ln (2 2 π) = ln (2) + ln (2 π)

= - ln (e) \frac{x}{2} - (ln (2) + ln (2 π))

\frac{x}{2} ln (e) = \frac{x}{2}

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

= - \frac{x}{2} - (\frac{1}{2} ln (2 π) + ln (2))

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

= - \frac{x}{2} - ln (2) - \frac{1}{2} ln (2 π)

Simplify

- \frac{x}{2} - ln (2) - \frac{1}{2} ln (2 π) : - ln (2) + \frac{- x - ln ( 2 π )}{2}

= - ln (2) + \frac{- x - ln ( 2 π )}{2}

ln (\frac{s + a}{s - b})

- lo g_{10} (3.3 (10)^{- 4})

2 ln (2) - ln (\frac{5}{3})

18200 (ln (0.58) - ln (1.3))

ln (2) + ln (35)

What is ln((e^{-x/2})/(2sqrt(2pi))) ?
The solution to ln((e^{-x/2})/(2sqrt(2pi))) is -ln(2)+(-x-ln(2pi))/2