What is log_{10}(sqrt(2))+log_{10}(\sqrt[3]{2}) ?

The solution to log_{10}(sqrt(2))+log_{10}(\sqrt[3]{2}) is 5/6 log_{10}(2)

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simplify log_{10}(sqrt(2))+log_{10}(\sqrt[3]{2})

simplify

\frac{5}{6} lo g_{10} (2)

Decimal Notation

0.25085 \dots

Solution steps

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

= lo g_{10} (2^{\frac{5}{6}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (2^{\frac{5}{6}}) = \frac{5}{6} lo g_{10} (2)

= \frac{5}{6} lo g_{10} (2)

- lo g_{10} (5.4 \cdot 1 0^{- 4})

ln (2 + e^{1}) - ln (2 + e^{- 3})

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 6)

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 3)

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

What is log_{10}(sqrt(2))+log_{10}(\sqrt[3]{2}) ?
The solution to log_{10}(sqrt(2))+log_{10}(\sqrt[3]{2}) is 5/6 log_{10}(2)