simplify 3ln(1/x)

Solution

simplify

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

- 3 ln (x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

= 3 (- ln (x) + 0)

Refine

= - 3 ln (x)

ln (8 x^{3})

lo g_{2} (x) - lo g_{2} (x^{7})

- \frac{1}{6} lo g_{2} (\frac{1}{6}) - \frac{5}{6} lo g_{2} (\frac{5}{6})

- lo g_{10} (7.4 \cdot 1 0^{- 4})

ln ((x y)^{3})