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Popular >

simplify 2ln(x)-4ln(1/y)-3ln(xy)

Solution

simplify

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

Solution

ln (\frac{y}{x})

Solution steps

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

Apply log rule:

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

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

= ln (x^{2}) - 4 ln (\frac{1}{y}) - 3 ln (x y)

Apply log rule:

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

4 ln (\frac{1}{y}) = ln ((\frac{1}{y})^{4})

= ln (x^{2}) - ln ((\frac{1}{y})^{4}) - 3 ln (x y)

Apply log rule:

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

ln (x^{2}) - ln ((\frac{1}{y})^{4}) = ln \frac{x ^{2}}{( \frac{1}{y} ) ^{4}}

= ln \frac{x ^{2}}{( \frac{1}{y} ) ^{4}} - 3 ln (x y)

Simplify

\frac{x ^{2}}{( \frac{1}{y} ) ^{4}} : x^{2} y^{4}

= ln (x^{2} y^{4}) - 3 ln (x y)

Apply log rule:

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

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

= ln (x^{2} y^{4}) - ln ((x y)^{3})

Apply log rule:

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

ln (x^{2} y^{4}) - ln ((x y)^{3}) = ln (\frac{x ^{2} y ^{4}}{( x y ) ^{3}})

= ln (\frac{x ^{2} y ^{4}}{( x y ) ^{3}})

Simplify

\frac{x ^{2} y ^{4}}{( x y ) ^{3}} : \frac{y}{x}

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

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Frequently Asked Questions (FAQ)

What is 2ln(x)-4ln(1/y)-3ln(xy) ?
The solution to 2ln(x)-4ln(1/y)-3ln(xy) is ln(y/x)