What is log_{e}(0.4p)-log_{e}(p) ?

The solution to log_{e}(0.4p)-log_{e}(p) is ln(0.4)

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simplify log_{e}(0.4p)-log_{e}(p)

simplify

lo g_{e} (0.4 p) - lo g_{e} (p)

ln (0.4)

Decimal Notation

- 0.91629 \dots

Solution steps

lo g_{e} (0.4 p) - lo g_{e} (p)

Apply log rule:

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

lo g_{e} (0.4 p) - lo g_{e} (p) = lo g_{e} (\frac{0.4 p}{p})

= lo g_{e} (\frac{0.4 p}{p})

Cancel the common factor:

p

= lo g_{e} (0.4)

Apply log rule:

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

= ln (0.4)

3 [2 ln (x - 1) - ln (x)] + ln (x + 1)

\frac{1}{8} ln (2)

ln (0.00006) - ln (0.00022)

ln (\frac{x - y}{y})

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

What is log_{e}(0.4p)-log_{e}(p) ?
The solution to log_{e}(0.4p)-log_{e}(p) is ln(0.4)