What is 1/2 ln(6/(1-e^{-6)}) ?

The solution to 1/2 ln(6/(1-e^{-6)}) is 1/2 (ln(6)-ln(1-1/(e^6)))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 ln(6/(1-e^{-6)})

simplify

\frac{1}{2} ln (\frac{6}{1 - e ^{- 6}})

\frac{1}{2} (ln (6) - ln (1 - \frac{1}{e ^{6}}))

Decimal Notation

0.89712 \dots

Solution steps

\frac{1}{2} ln (\frac{6}{1 - e ^{- 6}})

Apply log rule:

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

ln (\frac{6}{1 - e ^{- 6}}) = ln (6) - ln (1 - e^{- 6})

= \frac{1}{2} (ln (6) - ln (- e^{- 6} + 1))

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{2} (ln (6) - ln (- \frac{1}{e ^{6}} + 1))

lo g_{10} (5) + 2 lo g_{10} (x) + lo g_{10} (3)

ln (\frac{1}{x})

lo g_{10} (\frac{10 x}{6})

lo g_{b} (60) + lo g_{b} (3)

ln (p) - ln (p - 6500)

What is 1/2 ln(6/(1-e^{-6)}) ?
The solution to 1/2 ln(6/(1-e^{-6)}) is 1/2 (ln(6)-ln(1-1/(e^6)))