What is ln((\sqrt[6]{ab})/(c^3d)) ?

The solution to ln((\sqrt[6]{ab})/(c^3d)) is ln(\sqrt[6]{ab})-3ln(c)-ln(d)

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simplify ln((\sqrt[6]{ab})/(c^3d))

simplify

Solution steps

Apply log rule:

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

Apply log rule:

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

ln (c^{3} d) = ln (c^{3}) + ln (d)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (c^{3}) = 3 ln (c)

- (3 ln (c) + ln (d)) : - 3 ln (c) - ln (d)

2 lo g_{2} (3) + lo g_{2} (x)

ln (\frac{12}{\frac{7.02}{0.0445}})

5 lo g_{4} (a) + 6 lo g_{4} (b) - \frac{1}{3} lo g_{4} (7 c)

lo g_{10} (y) + lo g_{10} (z)

What is ln((\sqrt[6]{ab})/(c^3d)) ?
The solution to ln((\sqrt[6]{ab})/(c^3d)) is ln(\sqrt[6]{ab})-3ln(c)-ln(d)