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)/(11))

Solution

simplify

ln (\frac{e ^{3}}{11})

Solution

3 - ln (11)

+1

Decimal Notation

0.60210 \dots

Solution steps

ln (\frac{e ^{3}}{11})

Apply log rule:

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

ln (\frac{e ^{3}}{11}) = ln (e^{3}) - ln (11)

= ln (e^{3}) - ln (11)

Apply log rule:

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

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

= 3 ln (e) - ln (11)

3 ln (e) = 3

= 3 - ln (11)

Popular Examples

simplify 2ln(a)+3ln(b)simplify

2 ln (a) + 3 ln (b)

simplify ln(5x^3)simplify

ln (5 x^{3})

simplify ln(2)-ln(6)simplify

ln (2) - ln (6)

simplify log_{4}((64)/(sqrt(x+2)))simplify

lo g_{4} (\frac{64}{x + 2})

simplify-(1/3 log_{2}(1/3)+2/3 log_{2}(2/3))simplify

- (\frac{1}{3} lo g_{2} (\frac{1}{3}) + \frac{2}{3} lo g_{2} (\frac{2}{3}))

Frequently Asked Questions (FAQ)

What is ln((e^3)/(11)) ?
The solution to ln((e^3)/(11)) is 3-ln(11)