How do I expand In(m^2n^3)/(sqrt(p))?

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How do I expand In(m^2n^3)/(sqrt(p))?

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Answer 1 · 2017-12-19T14:53:14

The expression equals $2 ln m + 3 ln n - \frac{1}{2} ln p$ $2lnm +3lnn - 1/2lnp$ .

Explanation:

Remember you logarithm laws. Given $ln (\frac{m^{2} n^{3}}{\sqrt{p}})$ $ln((m^2n^3)/sqrt(p))$ , we can use $ln (a b) = ln a + ln b$ $ln(ab) = lna + lnb$ and $ln (\frac{a}{b}) = ln (a - b)$ $ln(a/b) = ln(a - b)$ . It's also helpful to know that $ln (a^{n}) = n ln a$ $ln(a^n) = nlna$ .

Therefore:

$= ln (m^{2}) + ln (n^{3}) - ln (\sqrt{p})$ $= ln(m^2) + ln(n^3) - ln(sqrt(p))$

$= 2 ln m + 3 ln n - \frac{1}{2} ln p \to$ $=2lnm + 3lnn - 1/2lnp ->$ because $\sqrt{x} = x^{\frac{1}{2}}$ $sqrt(x) = x^(1/2)$

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How do I expand In(m^2n^3)/(sqrt(p))?

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