en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(2)-3ln(3)

Solution

simplify

ln (2) - 3 ln (3)

Solution

ln (\frac{2}{27})

+1

Decimal Notation

- 2.60268 \dots

Solution steps

ln (2) - 3 ln (3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (2) - ln (3^{3})

Apply log rule:

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

ln (2) - ln (3^{3}) = ln (\frac{2}{3 ^{3}})

= ln (\frac{2}{3 ^{3}})

3^{3} = 27

= ln (\frac{2}{27})

Popular Examples

simplify 1/2 log_{c}(x)+5log_{c}(y)-2log_{c}(x)simplify

\frac{1}{2} lo g_{c} (x) + 5 lo g_{c} (y) - 2 lo g_{c} (x)

simplify 3ln(\sqrt[3]{t^2-1})-ln(t+1)simplify

simplify log_{5}(sqrt(x))-log_{5}(x^2)simplify

lo g_{5} (x) - lo g_{5} (x^{2})

simplify ln(2sqrt(2))simplify

ln (22)

simplify ln(x^2-81)-ln(x+9)simplify

ln (x^{2} - 81) - ln (x + 9)

Frequently Asked Questions (FAQ)

What is ln(2)-3ln(3) ?
The solution to ln(2)-3ln(3) is ln(2/27)