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Popular >

simplify 2ln(x)+3ln(y)-5ln(xy)

Solution

simplify

2 ln (x) + 3 ln (y) - 5 ln (x y)

Solution

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

Solution steps

2 ln (x) + 3 ln (y) - 5 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}) + 3 ln (y) - 5 ln (x y)

Apply log rule:

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

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

= ln (x^{2}) + ln (y^{3}) - 5 ln (x y)

Apply log rule:

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

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

= ln (x^{2} y^{3}) - 5 ln (x y)

Apply log rule:

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

5 ln (x y) = ln ((x y)^{5})

= ln (x^{2} y^{3}) - ln ((x y)^{5})

Apply log rule:

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

ln (x^{2} y^{3}) - ln ((x y)^{5}) = ln (\frac{x ^{2} y ^{3}}{( x y ) ^{5}})

= ln (\frac{x ^{2} y ^{3}}{( x y ) ^{5}})

Simplify

\frac{x ^{2} y ^{3}}{( x y ) ^{5}} : \frac{1}{x ^{3} y ^{2}}

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

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

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

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Frequently Asked Questions (FAQ)

What is 2ln(x)+3ln(y)-5ln(xy) ?
The solution to 2ln(x)+3ln(y)-5ln(xy) is -ln(x^3y^2)