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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

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

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

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

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ln (0. 1^{2} \cdot 0. 5^{2} \cdot 1^{2} \cdot 2^{2} \cdot 4^{2})

3 ln (b) - 3 ln (a)

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