What is ln(\sqrt[n]{2k+n})-ln(\sqrt[n]{k+2n}) ?

The solution to ln(\sqrt[n]{2k+n})-ln(\sqrt[n]{k+2n}) is ln(((2k+n)/(k+2n))^{1/n})

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simplify ln(\sqrt[n]{2k+n})-ln(\sqrt[n]{k+2n})

simplify

ln ((\frac{2 k + n}{k + 2 n})^{\frac{1}{n}})

Solution steps

Apply log rule:

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

Combine same powers :

= ln ((\frac{2 k + n}{k + 2 n})^{\frac{1}{n}})

ln ((θ + 1)^{n} \cdot (x^{θ}))

ln (7) 7

- lo g_{10} (1.541 \cdot 1 0^{- 5})

\frac{1}{3} ln (100) + \frac{2}{3} ln (200)

- ln (x) + 2 ln (x + 1) + 2 ln (x - 1)

What is ln(\sqrt[n]{2k+n})-ln(\sqrt[n]{k+2n}) ?
The solution to ln(\sqrt[n]{2k+n})-ln(\sqrt[n]{k+2n}) is ln(((2k+n)/(k+2n))^{1/n})