What is ln(3e^{a/(sqrt(2pi))}) ?

The solution to ln(3e^{a/(sqrt(2pi))}) is ln(3)+a/(2^{1/2)pi^{1/2}}

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simplify ln(3e^{a/(sqrt(2pi))})

simplify

ln (3 e^{\frac{a}{2 π}})

ln (3) + \frac{a}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

Solution steps

ln (3 e^{\frac{a}{2 π}})

Apply log rule:

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

ln (3 e^{\frac{a}{2 π}}) = ln (3) + ln (e^{\frac{a}{2 π}})

= ln (3) + ln (e^{\frac{a}{2 π}})

Apply log rule:

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

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

= ln (3) + \frac{a}{2 π} ln (e)

\frac{a}{2 π} ln (e) = \frac{a}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

= ln (3) + \frac{a}{2 ^{\frac{1}{2}} π ^{\frac{1}{2}}}

ln (11172) + 714 \cdot ln (8797)

ln (\frac{4}{3 ^{- 2} \cdot 5})

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ln (x ln (y - 2 x))

ln ((1) 5)

What is ln(3e^{a/(sqrt(2pi))}) ?
The solution to ln(3e^{a/(sqrt(2pi))}) is ln(3)+a/(2^{1/2)pi^{1/2}}