en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((e^3)/(1-e^3))

Solution

simplify

ln (\frac{e ^{3}}{1 - e ^{3}})

Solution

3 - ln (1 - e^{3})

Solution steps

ln (\frac{e ^{3}}{1 - e ^{3}})

Apply log rule:

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

ln (\frac{e ^{3}}{1 - e ^{3}}) = ln (e^{3}) - ln (1 - e^{3})

= ln (e^{3}) - ln (- e^{3} + 1)

Apply log rule:

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

ln (e^{3}) = 3 ln (e)

= 3 ln (e) - ln (1 - e^{3})

3 ln (e) = 3

= 3 - ln (- e^{3} + 1)

Popular Examples

simplify ln(t/5)simplify

ln (\frac{t}{5})

simplify ln(19)-ln(3)simplify

ln (19) - ln (3)

expand log_{3}((5x)^3)expand

lo g_{3} ((5 x)^{3})

simplify ln((5+0.5)/5)simplify

ln (\frac{5 + 0.5}{5})

simplify ln(29000/21000)simplify

ln (\frac{29000}{21000})

Frequently Asked Questions (FAQ)

What is ln((e^3)/(1-e^3)) ?
The solution to ln((e^3)/(1-e^3)) is 3-ln(1-e^3)