en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 5-ln(2)+ln(1/3)

Solution

simplify

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

Solution

5 - ln (6)

+1

Solution steps

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

Apply log rule:

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

ln (\frac{1}{3}) - ln (2) = ln (\frac{\frac{1}{3}}{2})

= 5 + ln (\frac{\frac{1}{3}}{2})

\frac{\frac{1}{3}}{2} = \frac{1}{6}

= 5 + ln (\frac{1}{6})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= 5 - ln (6)

Popular Examples

simplify 18ln(1/2)simplify

18 ln (\frac{1}{2})

simplify-log_{10}(1.3*10^{-11})simplify

- lo g_{10} (1.3 \cdot 1 0^{- 11})

simplify ln(4y-2)-ln(4y-4)simplify

ln (4 y - 2) - ln (4 y - 4)

simplify ln((e^{2x}-1)/(2e^x))simplify

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

simplify ln(69/119)simplify

ln (\frac{69}{119})

Frequently Asked Questions (FAQ)

What is 5-ln(2)+ln(1/3) ?
The solution to 5-ln(2)+ln(1/3) is 5-ln(6)