en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(6/(e^5))

Solution

simplify

ln (\frac{6}{e ^{5}})

Solution

ln (6) - 5

+1

Decimal Notation

- 3.20824 \dots

Solution steps

ln (\frac{6}{e ^{5}})

Apply log rule:

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

ln (\frac{6}{e ^{5}}) = ln (6) - ln (e^{5})

= ln (6) - ln (e^{5})

Apply log rule:

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

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

= ln (6) - 5 ln (e)

5 ln (e) = 5

= ln (6) - 5

Popular Examples

simplify 10log_{10}(i/(10^{-12)})simplify

10 lo g_{10} (\frac{i}{1 0 ^{- 12}})

simplify ln((e^3)/(10))simplify

ln (\frac{e ^{3}}{10})

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

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

simplify ln((2x-1)/(x^3))simplify

ln (\frac{2 x - 1}{x ^{3}})

simplify 2ln(x)+xln(3)-1/2 ln(x+1)simplify

2 ln (x) + x ln (3) - \frac{1}{2} ln (x + 1)

Frequently Asked Questions (FAQ)

What is ln(6/(e^5)) ?
The solution to ln(6/(e^5)) is ln(6)-5