en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((2e^5)/(1+e^5))

Solution

simplify

ln (\frac{2 e ^{5}}{1 + e ^{5}})

Solution

ln (2) + 5 - ln (1 + e^{5})

+1

Decimal Notation

0.68643 \dots

Solution steps

ln (\frac{2 e ^{5}}{1 + e ^{5}})

Apply log rule:

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

ln (\frac{2 e ^{5}}{1 + e ^{5}}) = ln (2 e^{5}) - ln (1 + e^{5})

= ln (2 e^{5}) - ln (e^{5} + 1)

Apply log rule:

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

ln (2 e^{5}) = ln (2) + ln (e^{5})

= ln (2) + ln (e^{5}) - ln (e^{5} + 1)

Apply log rule:

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

ln (e^{5}) = 5 ln (e)

= ln (2) + 5 ln (e) - ln (1 + e^{5})

5 ln (e) = 5

= ln (2) + 5 - ln (e^{5} + 1)

Popular Examples

simplify log_{10}(1/850)simplify

lo g_{10} (\frac{1}{850})

simplify ln(88/90)simplify

ln (\frac{88}{90})

simplify ln(6/5)+10 simplify

ln (\frac{6}{5}) + 10

expand ln((cb)/w)expand

ln (\frac{c b}{w})

simplify ln(x^2e^{2x-1})simplify

ln (x^{2} e^{2 x - 1})

Frequently Asked Questions (FAQ)

What is ln((2e^5)/(1+e^5)) ?
The solution to ln((2e^5)/(1+e^5)) is ln(2)+5-ln(1+e^5)