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)

2 lo g_{10} (ab)

lo g_{3} (8) - lo g_{3} (7)

2 lo g_{10} (c) - (3 lo g_{10} (a) + lo g_{10} (b))

10 lo g_{10} (1 0^{12} I)

lo g_{99} (\frac{9}{23}) + lo g_{99} (\frac{23}{9})

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