What is ln(x/(u^{2n)}e^{-(x^2)/(2nu^2)}) ?

The solution to ln(x/(u^{2n)}e^{-(x^2)/(2nu^2)}) is ln(x)-2nln(u)-(x^2)/(2nu^2)

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simplify ln(x/(u^{2n)}e^{-(x^2)/(2nu^2)})

simplify

ln (\frac{x}{u ^{2 n}} e^{- \frac{x ^{2}}{2 n u ^{2}}})

ln (x) - 2 n ln (u) - \frac{x ^{2}}{2 n u ^{2}}

Solution steps

ln (\frac{x}{u ^{2 n}} e^{- \frac{x ^{2}}{2 n u ^{2}}})

Apply log rule:

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

ln (\frac{x}{u ^{2 n}} e^{- \frac{x ^{2}}{2 n u ^{2}}}) = ln (\frac{x}{u ^{2 n}}) + ln (e^{- \frac{x ^{2}}{2 n u ^{2}}})

= ln (\frac{x}{u ^{2 n}}) + ln (e^{- \frac{x ^{2}}{2 n u ^{2}}})

Apply log rule:

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

ln (e^{- \frac{x ^{2}}{2 n u ^{2}}}) = - \frac{x ^{2}}{2 n u ^{2}} ln (e)

= ln (\frac{x}{u ^{2 n}}) - \frac{x ^{2}}{2 n u ^{2}} ln (e)

Apply log rule:

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

ln (\frac{x}{u ^{2 n}}) = ln (x) - ln (u^{2 n})

= ln (x) - ln (u^{2 n}) - ln (e) \frac{x ^{2}}{2 n u ^{2}}

Apply log rule:

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

ln (u^{2 n}) = 2 n ln (u)

= ln (x) - 2 n ln (u) - \frac{x ^{2}}{2 n u ^{2}} ln (e)

\frac{x ^{2}}{2 n u ^{2}} ln (e) = \frac{x ^{2}}{2 n u ^{2}}

= ln (x) - 2 n ln (u) - \frac{x ^{2}}{2 n u ^{2}}

3 lo g_{4} (x) + lo g_{4} (y)

\frac{1}{3} ln (6) - \frac{1}{3} ln (3)

ln (\frac{901.8 + 150}{1907.2 + 150})

- lo g_{10} (4.07 \cdot 1 0^{- 5})

3 ln (x y) + ln (y) - ln (x^{3} y)

What is ln(x/(u^{2n)}e^{-(x^2)/(2nu^2)}) ?
The solution to ln(x/(u^{2n)}e^{-(x^2)/(2nu^2)}) is ln(x)-2nln(u)-(x^2)/(2nu^2)