simplify ln(x/(3y))

Solution

simplify

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

ln (x) - ln (3) - ln (y)

Solution steps

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

Apply log rule:

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

ln (\frac{x}{3 y}) = ln (x) - ln (3 y)

= ln (x) - ln (3 y)

Apply log rule:

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

ln (3 y) = ln (3) + ln (y)

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

- (ln (3) + ln (y)) : - ln (3) - ln (y)

= ln (x) - ln (3) - ln (y)

lo g_{10} (9) + lo g_{10} (5) - lo g_{10} (15)

lo g_{10} (\frac{( a ^{6} b ^{3} )}{c ^{5}})

2 ln (x) + 6 ln (y) - 5 ln (z)

lo g_{3} (6) + lo g_{3} (2)

\frac{3}{2} (ln (x^{2} - 1) - ln (x + 1) + ln (x - 1))