simplify ln(1/(xc))

Solution

simplify

ln (\frac{1}{x c})

- (ln (x) + ln (c))

Solution steps

ln (\frac{1}{x c})

Apply log rule:

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

ln (\frac{1}{x c}) = ln (1) - ln (x c)

= ln (1) - ln (c x)

Apply log rule:

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

ln (x c) = ln (x) + ln (c)

= ln (1) - (ln (x) + ln (c))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (x) + ln (c))

0 - (ln (x) + ln (c)) = - (ln (x) + ln (c))

= - (ln (x) + ln (c))

\frac{1}{59049} \cdot ln^{- 1} (\frac{1}{3})

- \frac{1}{0.22} ln (\frac{1}{150})

ln (\frac{x + 4}{2})

lo g_{10} (\frac{1}{2 π})

\frac{1}{4} ln (5) + ln (2) - ln (3)