What is log_{e}((5y)/(x^3)) ?

The solution to log_{e}((5y)/(x^3)) is ln(5)+ln(y)-3ln(x)

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simplify log_{e}((5y)/(x^3))

simplify

lo g_{e} (\frac{5 y}{x ^{3}})

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

Solution steps

lo g_{e} (\frac{5 y}{x ^{3}})

Apply log rule:

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

lo g_{e} (\frac{5 y}{x ^{3}}) = lo g_{e} (5 y) - lo g_{e} (x^{3})

= lo g_{e} (5 y) - lo g_{e} (x^{3})

Apply log rule:

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

lo g_{e} (x^{3}) = 3 lo g_{e} (x)

= lo g_{e} (5 y) - 3 lo g_{e} (x)

Apply log rule:

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

lo g_{e} (5 y) = lo g_{e} (5) + lo g_{e} (y)

= lo g_{e} (5) + lo g_{e} (y) - 3 lo g_{e} (x)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (5) + lo g_{e} (y) - 3 lo g_{e} (x)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (5) + ln (y) - 3 lo g_{e} (x)

Simplify

lo g_{e} (x) : ln (x)

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

ln (x^{4} e^{- x})

5 ln (5) - 4 ln (4) - 3 ln (3)

ln (\frac{47}{37})

ln (p) - ln (1 - p)

ln (3.26 \cdot 10)

What is log_{e}((5y)/(x^3)) ?
The solution to log_{e}((5y)/(x^3)) is ln(5)+ln(y)-3ln(x)