What is ln(x^6)-5ln(\sqrt[5]{x^4}) ?

The solution to ln(x^6)-5ln(\sqrt[5]{x^4}) is ln(x^2)

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simplify ln(x^6)-5ln(\sqrt[5]{x^4})

simplify

ln (x^{2})

Solution steps

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 (x^{2})

2 ln (a) - \frac{1}{3} ln (b) + 3 ln (c)

lo g_{10} (\frac{4 c}{3})

lo g_{10} (\frac{1000}{m ^{2} + n ^{2}})

lo g_{4} (3 x y)

5 lo g_{5} (x) - \frac{1}{4} lo g_{5} (8 - x)

What is ln(x^6)-5ln(\sqrt[5]{x^4}) ?
The solution to ln(x^6)-5ln(\sqrt[5]{x^4}) is ln(x^2)