What is ln(xy)+ln(xy^2)-ln(x) ?

The solution to ln(xy)+ln(xy^2)-ln(x) is ln(xy^3)

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simplify ln(xy)+ln(xy^2)-ln(x)

simplify

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

ln (x y^{3})

Solution steps

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

Apply log rule:

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

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

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

Simplify

x y x y^{2} : x^{2} y^{3}

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

Apply log rule:

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

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

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

Cancel the common factor:

x

= ln (x y^{3})

2 ln (x - 1) - ln (x + 2)

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

ln (\frac{3 - x}{3 + x})

(\frac{1}{2}) ln (cos^{2} (x))

ln (\frac{2 ^{- 3}}{1125})

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