What is ln(1000)+ln(1/e)+log_{3}(27) ?

The solution to ln(1000)+ln(1/e)+log_{3}(27) is ln(1000)++ln(1)-ln(e)+log_{3}(27)

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simplify ln(1000)+ln(1/e)+log_{3}(27)

simplify

ln (1000) + ln (\frac{1}{e}) + lo g_{3} (27)

ln (1000) + + ln (1) - ln (e) + lo g_{3} (27)

Decimal Notation

8.90775 \dots

Solution steps

ln (1000) + ln (\frac{1}{e}) + lo g_{3} (27)

Apply log rule:

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

ln (\frac{1}{e}) = ln (1) - ln (e)

= ln (1000) + + ln (1) - ln (e) + lo g_{3} (27)

ln (\frac{1}{1 + 3})

lo g_{10} (8 x^{2} yz)

lo g_{10} (\frac{3 x ^{2}}{2})

- ln (\frac{e ^{2} - 1}{2 e ^{2}})

lo g_{2} (A) + lo g_{2} (B)

What is ln(1000)+ln(1/e)+log_{3}(27) ?
The solution to ln(1000)+ln(1/e)+log_{3}(27) is ln(1000)++ln(1)-ln(e)+log_{3}(27)