What is ln((5w^2v)/(x+y)) ?

The solution to ln((5w^2v)/(x+y)) is ln(5)+2ln(w)+ln(v)-ln(x+y)

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simplify ln((5w^2v)/(x+y))

simplify

ln (\frac{5 w ^{2} v}{x + y})

ln (5) + 2 ln (w) + ln (v) - ln (x + y)

Solution steps

ln (\frac{5 w ^{2} v}{x + y})

Apply log rule:

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

ln (\frac{5 w ^{2} v}{x + y}) = ln (5 w^{2} v) - ln (x + y)

= ln (5 v w^{2}) - ln (x + y)

Apply log rule:

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

ln (5 w^{2} v) = ln (5) + ln (w^{2}) + ln (v)

= ln (5) + ln (w^{2}) + ln (v) - ln (x + y)

Apply log rule:

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

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

= ln (5) + 2 ln (w) + ln (v) - ln (x + y)

ln_{e} (x^{\frac{1}{8}})

\frac{1}{5} x^{5} (ln (3) + 2 ln (x))

ln (\frac{400}{250})

ln (x^{3} e^{x})

lo g_{e} (12) - lo g_{e} (6)

What is ln((5w^2v)/(x+y)) ?
The solution to ln((5w^2v)/(x+y)) is ln(5)+2ln(w)+ln(v)-ln(x+y)