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

The solution to ln((x^pe(-y))/(sqrt(z))) is pln(x)+1+ln(-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) + 1 + ln (- 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 x^{p} (- y)) - 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) + ln (- y)

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

Apply log rule:

lo g_{a} (a) = 1

= p ln (x) + 1 + ln (- y) - ln (z)

2 ln (\frac{2}{5})

2 lo g_{7} (x + 2) - lo g_{7} (x^{2} - 4)

ln (\frac{s ^{2} + a ^{2}}{s ^{2} + b ^{2}})

lo g_{3} (x) + 2 lo g_{3} ((x + 1)^{2}) - lo g_{3} (81)

ln (\frac{( x ^{4} y )}{3 z ^{5}})

What is ln((x^pe(-y))/(sqrt(z))) ?
The solution to ln((x^pe(-y))/(sqrt(z))) is pln(x)+1+ln(-y)-ln(sqrt(z))