en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((m^3)/n)

Solution

simplify

ln (\frac{m ^{3}}{n})

Solution

3 ln (m) - ln (n)

Solution steps

ln (\frac{m ^{3}}{n})

Apply log rule:

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

ln (\frac{m ^{3}}{n}) = ln (m^{3}) - ln (n)

= ln (m^{3}) - ln (n)

Apply log rule:

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

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

= 3 ln (m) - ln (n)

Popular Examples

simplify ln(200)-ln(100)simplify

ln (200) - ln (100)

simplify ln((y^5)/3)simplify

ln (\frac{y ^{5}}{3})

simplify (-1)/2 ln(1/2)simplify

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

expand log_{10}(yx^5)expand

lo g_{10} (y x^{5})

simplify ln(37/30)simplify

ln (\frac{37}{30})

Frequently Asked Questions (FAQ)

What is ln((m^3)/n) ?
The solution to ln((m^3)/n) is 3ln(m)-ln(n)