en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((e^6)/6)

Solution

simplify

ln (\frac{e ^{6}}{6})

Solution

6 - ln (6)

+1

Decimal Notation

4.20824 \dots

Solution steps

ln (\frac{e ^{6}}{6})

Apply log rule:

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

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

= ln (e^{6}) - ln (6)

Apply log rule:

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

ln (e^{6}) = 6 ln (e)

= 6 ln (e) - ln (6)

6 ln (e) = 6

= 6 - ln (6)

Popular Examples

simplify log_{a}((x^2y)/(a^3z^4))simplify

lo g_{a} (\frac{x ^{2} y}{a ^{3} z ^{4}})

simplify log_{b}(20)-2log_{b}(2)+3 simplify

lo g_{b} (20) - 2 lo g_{b} (2) + 3

simplify log_{4}(6)+log_{4}(9)simplify

lo g_{4} (6) + lo g_{4} (9)

simplify 5ln(x)-1/8 ln(y)simplify

5 ln (x) - \frac{1}{8} ln (y)

simplify ln(27/25)simplify

ln (\frac{27}{25})

Frequently Asked Questions (FAQ)

What is ln((e^6)/6) ?
The solution to ln((e^6)/6) is 6-ln(6)