en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(3)+ln(6)-ln(9)

Solution

simplify

ln (3) + ln (6) - ln (9)

Solution

ln (2)

+1

Decimal Notation

0.69314 \dots

Solution steps

ln (3) + ln (6) - ln (9)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (3) + ln (6) = ln (3 \cdot 6)

= ln (3 \cdot 6) - ln (9)

Multiply the numbers:

3 \cdot 6 = 18

= ln (18) - ln (9)

Apply log rule:

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

ln (18) - ln (9) = ln (\frac{18}{9})

= ln (\frac{18}{9})

Divide the numbers:

\frac{18}{9} = 2

= ln (2)

Popular Examples

simplify ln(((x+1))/(x-1))simplify

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

simplify-log_{10}(1.26*10^{-6})simplify

- lo g_{10} (1.26 \cdot 1 0^{- 6})

simplify 4ln(3x^2)-1/2 ln(9x^8)simplify

4 ln (3 x^{2}) - \frac{1}{2} ln (9 x^{8})

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

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

simplify ln((a^4)/(b^{-4)c^3})simplify

ln (\frac{a ^{4}}{b ^{- 4} c ^{3}})

Frequently Asked Questions (FAQ)

What is ln(3)+ln(6)-ln(9) ?
The solution to ln(3)+ln(6)-ln(9) is ln(2)