What is log_{e}(2/3 w) ?

The solution to log_{e}(2/3 w) is ln(2)-ln(3)+ln(w)

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simplify log_{e}(2/3 w)

simplify

lo g_{e} (\frac{2}{3} w)

ln (2) - ln (3) + ln (w)

Solution steps

lo g_{e} (\frac{2}{3} w)

Apply log rule:

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

lo g_{e} (\frac{2}{3} w) = lo g_{e} (\frac{2}{3}) + lo g_{e} (w)

= lo g_{e} (\frac{2}{3}) + lo g_{e} (w)

Apply log rule:

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

lo g_{e} (\frac{2}{3}) = lo g_{e} (2) - lo g_{e} (3)

= lo g_{e} (2) - lo g_{e} (3) + lo g_{e} (w)

Apply log rule:

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

= ln (2) - lo g_{e} (3) + lo g_{e} (w)

Apply log rule:

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

= ln (2) - ln (3) + lo g_{e} (w)

Apply log rule:

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

= ln (2) - ln (3) + ln (w)

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