What is ln(((x^pe^{-y}))/(sqrt(z))) ?

The solution to ln(((x^pe^{-y}))/(sqrt(z))) is pln(x)-y-ln(sqrt(z))

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simplify ln(((x^pe^{-y}))/(sqrt(z)))

simplify

ln (\frac{( x ^{p} e ^{- y} )}{z})

p ln (x) - y - ln (z)

Solution steps

ln (\frac{( x ^{p} e ^{- y} )}{z})

Apply log rule:

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

ln (\frac{( x ^{p} e ^{- y} )}{z}) = ln ((x^{p} e^{- y})) - ln (z)

= ln (e^{- y} x^{p}) - ln (z)

Apply log rule:

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

ln (x^{p} e^{- y}) = ln (x^{p}) + ln (e^{- y})

= ln (x^{p}) + ln (e^{- y}) - ln (z)

Apply log rule:

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

ln (x^{p}) = p ln (x)

= p ln (x) + ln (e^{- y}) - ln (z)

Apply log rule:

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

ln (e^{- y}) = - y ln (e)

= p ln (x) - y ln (e) - ln (z)

y ln (e) = y

= p ln (x) - y - ln (z)

lo g_{10}^{2} (8) - lo g_{10}^{2} (125)

ln (x + 9) + ln (x - 9)

lo g_{4} (\frac{3 a ^{7} c}{5})

ln (x) - ln (7)

lo g_{2} (\frac{x ^{3} y ^{2}}{z})

What is ln(((x^pe^{-y}))/(sqrt(z))) ?
The solution to ln(((x^pe^{-y}))/(sqrt(z))) is pln(x)-y-ln(sqrt(z))