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)

ln (x^{5} y^{3})

lo g_{10} (5 + x) - 2 lo g_{10} (x + 4)

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

lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x + 1)

lo g_{10} (x) - 2 lo g_{10} (y) + 3 lo g_{10} (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))