en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 3ln(x)-5ln(1/y)-4ln(xy)

Solution

simplify

3 ln (x) - 5 ln (\frac{1}{y}) - 4 ln (x y)

Solution

ln (\frac{y}{x})

Solution steps

3 ln (x) - 5 ln (\frac{1}{y}) - 4 ln (x y)

Apply log rule:

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

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

= ln (x^{3}) - 5 ln (\frac{1}{y}) - 4 ln (x y)

Apply log rule:

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

5 ln (\frac{1}{y}) = ln ((\frac{1}{y})^{5})

= ln (x^{3}) - ln ((\frac{1}{y})^{5}) - 4 ln (x y)

Apply log rule:

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

ln (x^{3}) - ln ((\frac{1}{y})^{5}) = ln \frac{x ^{3}}{( \frac{1}{y} ) ^{5}}

= ln \frac{x ^{3}}{( \frac{1}{y} ) ^{5}} - 4 ln (x y)

Simplify

\frac{x ^{3}}{( \frac{1}{y} ) ^{5}} : x^{3} y^{5}

= ln (x^{3} y^{5}) - 4 ln (x y)

Apply log rule:

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

4 ln (x y) = ln ((x y)^{4})

= ln (x^{3} y^{5}) - ln ((x y)^{4})

Apply log rule:

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

ln (x^{3} y^{5}) - ln ((x y)^{4}) = ln (\frac{x ^{3} y ^{5}}{( x y ) ^{4}})

= ln (\frac{x ^{3} y ^{5}}{( x y ) ^{4}})

Simplify

\frac{x ^{3} y ^{5}}{( x y ) ^{4}} : \frac{y}{x}

= ln (\frac{y}{x})

Popular Examples

simplify log_{8}(x*y*z^6)simplify

lo g_{8} (x \cdot y \cdot z^{6})

simplify log_{2}((x^6y^7)/8)simplify

lo g_{2} (\frac{x ^{6} y ^{7}}{8})

simplify 2log_{5}(a)-4log_{5}(b)simplify

2 lo g_{5} (a) - 4 lo g_{5} (b)

simplify log_{10}(2)-log_{10}(14)simplify

lo g_{10} (2) - lo g_{10} (14)

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

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

Frequently Asked Questions (FAQ)

What is 3ln(x)-5ln(1/y)-4ln(xy) ?
The solution to 3ln(x)-5ln(1/y)-4ln(xy) is ln(y/x)