What is ln(y^3)-ln(y)-ln(y^6) ?

The solution to ln(y^3)-ln(y)-ln(y^6) is -ln(y^4)

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simplify ln(y^3)-ln(y)-ln(y^6)

simplify

ln (y^{3}) - ln (y) - ln (y^{6})

- ln (y^{4})

Solution steps

ln (y^{3}) - ln (y) - ln (y^{6})

Apply log rule:

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

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

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

Cancel the common factor:

y

= ln (y^{2}) - ln (y^{6})

Apply log rule:

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

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

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

Simplify

\frac{y ^{2}}{y ^{6}} : \frac{1}{y ^{4}}

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

Apply log rule:

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

= - ln (y^{4})

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What is ln(y^3)-ln(y)-ln(y^6) ?
The solution to ln(y^3)-ln(y)-ln(y^6) is -ln(y^4)