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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (\frac{x}{a}) = ln (x) - ln (a)

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

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

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

lo g_{10} (\frac{x ( x + 7 )}{( x + 3 ) ^{4}})

\frac{1}{2} lo g_{4} (16 x)

lo g_{0.5} (x + 1) - lo g_{0.5} (x - 3)

2 lo g_{6} (x - 7) + lo g_{6} (9) - 2

3 lo g_{10} (3) - 3 lo g_{10} (x)

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