en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 6ln(x)-1/3 ln(y)

Solution

simplify

6 ln (x) - \frac{1}{3} ln (y)

Solution

ln (\frac{x ^{6} y ^{\frac{2}{3}}}{y})

Solution steps

6 ln (x) - \frac{1}{3} ln (y)

Apply log rule:

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

6 ln (x) = ln (x^{6})

= ln (x^{6}) - \frac{1}{3} ln (y)

Apply log rule:

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

\frac{1}{3} ln (y) = ln (y^{\frac{1}{3}})

= ln (x^{6}) - ln (y^{\frac{1}{3}})

Apply log rule:

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

ln (x^{6}) - ln (y^{\frac{1}{3}}) = ln (\frac{x ^{6}}{y ^{\frac{1}{3}}})

= ln (\frac{x ^{6}}{y ^{\frac{1}{3}}})

Simplify

\frac{x ^{6}}{y ^{\frac{1}{3}}} : \frac{x ^{6} y ^{\frac{2}{3}}}{y}

= ln (\frac{x ^{6} y ^{\frac{2}{3}}}{y})

Popular Examples

simplify log_{10}(sqrt(7)z)simplify

lo g_{10} (7 z)

simplify ln(3x^5)simplify

ln (3 x^{5})

simplify log_{3}(9/(sqrt(x+3)))simplify

lo g_{3} (\frac{9}{x + 3})

simplify-5log_{2}(x+1)+3log_{2}(6x)simplify

- 5 lo g_{2} (x + 1) + 3 lo g_{2} (6 x)

join 1/2 log_{2}(7)join

\frac{1}{2} lo g_{2} (7)

Frequently Asked Questions (FAQ)

What is 6ln(x)-1/3 ln(y) ?
The solution to 6ln(x)-1/3 ln(y) is ln((x^6y^{2/3})/y)