simplify ln(1/2 x)

Solution

simplify

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

ln (x) - ln (2)

Solution steps

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

Apply log rule:

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

ln (\frac{1}{2} x) = ln (\frac{1}{2}) + ln (x)

= ln (\frac{1}{2}) + ln (x)

Apply log rule:

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

ln (\frac{1}{2}) = ln (1) - ln (2)

= ln (1) - ln (2) + ln (x)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2) + ln (x)

0 - ln (2) + ln (x) = - ln (2) + ln (x)

= ln (x) - ln (2)

5 ln (x) - \frac{5}{3} ln (y) - 6 ln (w^{2}) + 9 ln (z)

lo g_{5} (3 x)

\frac{1}{2} lo g_{10} (a) + 3 lo g_{10} (b)

lo g_{3} (x + 1) - lo g_{3} (x^{2} - 1)

lo g_{b} (z^{6} y)