What is ln(x^6)-3ln(\sqrt[3]{x^2}) ?

The solution to ln(x^6)-3ln(\sqrt[3]{x^2}) is ln(x^4)

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simplify ln(x^6)-3ln(\sqrt[3]{x^2})

simplify

ln (x^{4})

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^{4})

3 ln (x + 1) + 2 ln (6 - x) + \frac{1}{3} ln (2 x + 1)

5 ln (2 e)

ln (22) + ln (2)

9 lo g_{5} (x) + lo g_{5} (y)

5 ln (3 x)

What is ln(x^6)-3ln(\sqrt[3]{x^2}) ?
The solution to ln(x^6)-3ln(\sqrt[3]{x^2}) is ln(x^4)