simplify ln(1/3 x)

Solution

simplify

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

ln (x) - ln (3)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (\frac{1}{3}) = ln (1) - ln (3)

= ln (1) - ln (3) + ln (x)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (3) + ln (x)

0 - ln (3) + ln (x) = - ln (3) + ln (x)

= ln (x) - ln (3)

- 4 (ln (4 + 16 - x^{2}) - ln (x))

ln (\frac{- x ^{2}}{2})

\frac{1}{75} ln (\frac{1}{2})

\frac{100}{2 \cdot π \cdot 100} \cdot ln (\frac{4 + 2 \cdot 10 0 ^{2}}{25})

ln (\frac{0.1524}{k} \cdot 3.71)