What is ln(1/e)+ln(AB) ?

The solution to ln(1/e)+ln(AB) is ln(A)+ln(B)-1

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simplify ln(1/e)+ln(AB)

simplify

ln (\frac{1}{e}) + ln (A B)

ln (A) + ln (B) - 1

Solution steps

ln (\frac{1}{e}) + ln (A B)

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 (1) - ln (e) + ln (A B)

Apply log rule:

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

ln (A B) = ln (A) + ln (B)

= ln (1) - ln (e) + ln (A) + ln (B)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (e) + ln (A) + ln (B)

Apply log rule:

lo g_{a} (a) = 1

= 0 - 1 + ln (A) + ln (B)

Subtract the numbers:

0 - 1 = - 1

= ln (A) + ln (B) - 1

ln (2.33 \cdot 1 0^{- 2})

ln (\frac{760}{102})

ln (\frac{11.9}{1252})

3 lo g_{10} (x) - lo g_{10} (4 y)

ln (6) + ln (30)