What is log_{e}(4xy) ?

The solution to log_{e}(4xy) is 2ln(2)+ln(x)+ln(y)

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simplify log_{e}(4xy)

simplify

lo g_{e} (4 x y)

2 ln (2) + ln (x) + ln (y)

Solution steps

lo g_{e} (4 x y)

Apply log rule:

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

lo g_{e} (4 x y) = lo g_{e} (4) + lo g_{e} (x) + lo g_{e} (y)

= lo g_{e} (4) + lo g_{e} (x) + lo g_{e} (y)

Apply log rule:

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

= ln (4) + lo g_{e} (x) + lo g_{e} (y)

Apply log rule:

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

= ln (4) + ln (x) + lo g_{e} (y)

Apply log rule:

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

= ln (4) + ln (x) + ln (y)

ln (4) = 2 ln (2)

= 2 ln (2) + ln (x) + ln (y)

ln (\frac{u ^{2} + u ^{2} - a ^{2}}{a})

\frac{1}{5} ln (\frac{15}{24})

- \frac{1}{5} lo g_{10} (y + 3) + \frac{1}{5} lo g_{10} (y - 2)

4 lo g_{10} (x - 7) - 5 lo g_{10} (x)

- \frac{1}{3} ln ∣ x + 1 ∣ + \frac{1}{3} ln ∣ x - 2 ∣