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

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

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

simplify

\frac{5}{6} ln (2)

Decimal Notation

0.57762 \dots

Solution steps

Apply log rule:

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

= ln (2^{\frac{5}{6}})

Apply log rule

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

assuming

x \geq 0

= \frac{5}{6} ln (2)

3 lo g_{b} (y) - \frac{7}{2} lo g_{b} (x)

ln (e^{x}) + ln (- 1)

\frac{1}{2} ln (\frac{39}{59})

lo g_{10} (f (x) (\frac{cos ( x )}{x ^{2} + cos ( x )}))

ln (\frac{1}{5 n + 8}) + ln (7 n + 5)

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