en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x^3)/(7y^2))

Solution

simplify

ln (\frac{x ^{3}}{7 y ^{2}})

Solution

3 ln (x) - ln (7) - 2 ln (y)

Solution steps

ln (\frac{x ^{3}}{7 y ^{2}})

Apply log rule:

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

ln (\frac{x ^{3}}{7 y ^{2}}) = ln (x^{3}) - ln (7 y^{2})

= ln (x^{3}) - ln (7 y^{2})

Apply log rule:

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

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

= 3 ln (x) - ln (7 y^{2})

Apply log rule:

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

ln (7 y^{2}) = ln (7) + ln (y^{2})

= 3 ln (x) - (ln (y^{2}) + ln (7))

Apply log rule:

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

ln (y^{2}) = 2 ln (y)

= 3 ln (x) - (ln (7) + 2 ln (y))

- (ln (7) + 2 ln (y)) : - ln (7) - 2 ln (y)

= 3 ln (x) - ln (7) - 2 ln (y)

Popular Examples

simplify ln(1/(0.95))simplify

ln (\frac{1}{0.95})

simplify ln((e^2-e^4)/(x^2+7x+6))simplify

ln (\frac{e ^{2} - e ^{4}}{x ^{2} + 7 x + 6})

simplify log_{10}((3x^3\sqrt[4]{4-x})/(4(x+4)^2))simplify

simplify 3log_{5}(u)+7log_{5}(v)simplify

3 lo g_{5} (u) + 7 lo g_{5} (v)

simplify log_{b}(3/7)simplify

lo g_{b} (\frac{3}{7})

Frequently Asked Questions (FAQ)

What is ln((x^3)/(7y^2)) ?
The solution to ln((x^3)/(7y^2)) is 3ln(x)-ln(7)-2ln(y)