simplify ln(x/(2y))

Solution

simplify

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

ln (x) - ln (2) - ln (y)

Solution steps

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

Apply log rule:

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

ln (\frac{x}{2 y}) = ln (x) - ln (2 y)

= ln (x) - ln (2 y)

Apply log rule:

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

ln (2 y) = ln (2) + ln (y)

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

- (ln (2) + ln (y)) : - ln (2) - ln (y)

= ln (x) - ln (2) - ln (y)

ln ∣ x ∣ + ln cos (\frac{y}{x})

\frac{1}{6} ln x^{2} + 9 + \frac{1}{6} ln \frac{x ^{2}}{9} + 1

ln (\frac{x ^{4}}{y ^{5}})

lo g_{3} (\frac{a ^{5} b}{c ^{2}})

2 ln (5) - 2 ln (3)