What is 2ln(sqrt(x^3))-5ln(\sqrt[5]{y^4}) ?

The solution to 2ln(sqrt(x^3))-5ln(\sqrt[5]{y^4}) is ln((x^3)/(y^4))

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simplify 2ln(sqrt(x^3))-5ln(\sqrt[5]{y^4})

simplify

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

Solution steps

Apply log rule:

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

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

Apply log rule:

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

Apply log rule:

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

Simplify

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

lo g_{5} (3) - lo g_{5} (4)

ln (y) - 2 ln (x)

ln (\frac{e ^{2}}{4})

lo g_{a} (\frac{x ^{3}}{y z ^{4}})

ln (x^{14} \frac{y ^{17}}{z ^{13}})

What is 2ln(sqrt(x^3))-5ln(\sqrt[5]{y^4}) ?
The solution to 2ln(sqrt(x^3))-5ln(\sqrt[5]{y^4}) is ln((x^3)/(y^4))