What is log_{e}(3^{1/6})+log_{e}(6^{1/3}) ?

The solution to log_{e}(3^{1/6})+log_{e}(6^{1/3}) is ln(3^{1/2}*2^{1/3})

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simplify log_{e}(3^{1/6})+log_{e}(6^{1/3})

simplify

lo g_{e} (3^{\frac{1}{6}}) + lo g_{e} (6^{\frac{1}{3}})

ln (3^{\frac{1}{2}} \cdot 2^{\frac{1}{3}})

Decimal Notation

0.78035 \dots

Solution steps

lo g_{e} (3^{\frac{1}{6}}) + lo g_{e} (6^{\frac{1}{3}})

Apply log rule:

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

lo g_{e} (3^{\frac{1}{6}}) + lo g_{e} (6^{\frac{1}{3}}) = lo g_{e} (3^{\frac{1}{6}} \cdot 6^{\frac{1}{3}})

= lo g_{e} (3^{\frac{1}{6}} \cdot 6^{\frac{1}{3}})

3^{\frac{1}{6}} \cdot 6^{\frac{1}{3}} = 3^{\frac{1}{2}} \cdot 2^{\frac{1}{3}}

= lo g_{e} (3^{\frac{1}{2}} \cdot 2^{\frac{1}{3}})

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (3^{\frac{1}{2}} \cdot 2^{\frac{1}{3}})

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

5 lo g_{10} (x) + lo g_{10} (7)

ln (\frac{y ^{2}}{x ^{2}})

- lo g_{10} (4.907 \cdot 1 0^{- 3})

ln (\frac{a}{b + c})

What is log_{e}(3^{1/6})+log_{e}(6^{1/3}) ?
The solution to log_{e}(3^{1/6})+log_{e}(6^{1/3}) is ln(3^{1/2}*2^{1/3})