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} (\frac{a ^{3} b ^{3}}{c ^{4}})

ln (\frac{5 y ^{2} x}{z ^{3}})

lo g_{7} (\frac{1}{7} a^{3} b)

lo g_{10} (\frac{z ^{3} x ^{4}}{y})

lo g_{10} (x^{6}) - lo g_{10} (x^{5})

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