What is log_{e}(8000)-log_{e}(4000) ?

The solution to log_{e}(8000)-log_{e}(4000) is ln(2)

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simplify log_{e}(8000)-log_{e}(4000)

simplify

lo g_{e} (8000) - lo g_{e} (4000)

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

lo g_{e} (8000) - lo g_{e} (4000)

Apply log rule:

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

lo g_{e} (8000) - lo g_{e} (4000) = lo g_{e} (\frac{8000}{4000})

= lo g_{e} (\frac{8000}{4000})

Divide the numbers:

\frac{8000}{4000} = 2

= lo g_{e} (2)

Apply log rule:

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

= ln (2)

ln (y) + ln (c)

- 5 ln (3 x)

lo g_{e} (3 x^{2})

ln (x e^{v})

\frac{1}{4} ln (30 x)

What is log_{e}(8000)-log_{e}(4000) ?
The solution to log_{e}(8000)-log_{e}(4000) is ln(2)