simplify ln(N/(No))

Solution

simplify

ln (\frac{N}{N o})

- ln (o)

Solution steps

ln (\frac{N}{N o})

Apply log rule:

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

ln (\frac{N}{N o}) = ln (N) - ln (N o)

= ln (N) - ln (N o)

Apply log rule:

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

ln (N o) = ln (N) + ln (o)

= ln (N) - (ln (o) + ln (N))

- (ln (N) + ln (o)) : - ln (N) - ln (o)

= ln (N) - ln (N) - ln (o)

Add similar elements:

ln (N) - ln (N) = 0

= - ln (o)

ln (3.8) + ln (9.4)

ln (\frac{66}{78})

ln (a) - 3 ln (b) + 5 ln (c)

ln (- R) + ln (R 2)

- lo g_{10} (1 \cdot 1 0^{- 0.9})