What is ln((x^2sqrt(y))/(4e^5y^3)) ?

The solution to ln((x^2sqrt(y))/(4e^5y^3)) is 2ln(x)+ln(sqrt(y))-2ln(2)-5-3ln(y)

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simplify ln((x^2sqrt(y))/(4e^5y^3))

simplify

ln (\frac{x ^{2} y}{4 e ^{5} y ^{3}})

2 ln (x) + ln (y) - 2 ln (2) - 5 - 3 ln (y)

Solution steps

ln (\frac{x ^{2} y}{4 e ^{5} y ^{3}})

Apply log rule:

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

ln (\frac{x ^{2} y}{4 e ^{5} y ^{3}}) = ln (x^{2} y) - ln (4 e^{5} y^{3})

= ln (x^{2} y) - ln (4 e^{5} y^{3})

Apply log rule:

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

ln (x^{2} y) = ln (x^{2}) + ln (y), ln (4 e^{5} y^{3}) = ln (4) + ln (e^{5}) + ln (y^{3})

= ln (x^{2}) + ln (y) - (ln (y^{3}) + ln (4) + ln (e^{5}))

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= 2 ln (x) + ln (y) - (ln (4) + ln (e^{5}) + ln (y^{3}))

Apply log rule:

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

ln (e^{5}) = 5 ln (e)

= 2 ln (x) + ln (y) - (ln (4) + 5 ln (e) + ln (y^{3}))

Apply log rule:

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

ln (y^{3}) = 3 ln (y)

= 2 ln (x) + ln (y) - (ln (4) + 5 ln (e) + 3 ln (y))

- (ln (4) + 5 ln (e) + 3 ln (y)) = - (2 ln (2) + 5 + 3 ln (y))

= 2 ln (x) + ln (y) - (3 ln (y) + 2 ln (2) + 5)

- (2 ln (2) + 5 + 3 ln (y)) : - 2 ln (2) - 5 - 3 ln (y)

= 2 ln (x) + ln (y) - 2 ln (2) - 5 - 3 ln (y)

ln (x^{2}) + 2 ln (x) + 1

\frac{1}{0.04} ln (\frac{72}{72 - 42})

ln (\frac{y ^{x} \cdot e ^{- y}}{x !})

ln (\frac{4 x + 1}{3 x - 1})

ln (\frac{3 x ^{2}}{x ^{2} + 4})

What is ln((x^2sqrt(y))/(4e^5y^3)) ?
The solution to ln((x^2sqrt(y))/(4e^5y^3)) is 2ln(x)+ln(sqrt(y))-2ln(2)-5-3ln(y)