en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((e^5)/5)

Solution

simplify

ln (\frac{e ^{5}}{5})

Solution

5 - ln (5)

+1

Decimal Notation

3.39056 \dots

Solution steps

ln (\frac{e ^{5}}{5})

Apply log rule:

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

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

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

Apply log rule:

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

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

= 5 ln (e) - ln (5)

5 ln (e) = 5

= 5 - ln (5)

Popular Examples

simplify log_{3}(x)+log_{3}(x+4)simplify

lo g_{3} (x) + lo g_{3} (x + 4)

simplify log_{10}((ab^3)/(c^2))simplify

lo g_{10} (\frac{a b ^{3}}{c ^{2}})

simplify ln(3)-ln(x)simplify

ln (3) - ln (x)

simplify 7/2 ln(ln(e^x))-ln(sqrt(e^{6ln(x))})simplify

\frac{7}{2} ln (ln (e^{x})) - ln (e^{6 l n (x)})

simplify log_{5}((a^3)/(b^3))simplify

lo g_{5} (\frac{a ^{3}}{b ^{3}})

Frequently Asked Questions (FAQ)

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