simplify ln((2x)/3)

Solution

simplify

ln (\frac{2 x}{3})

ln (2) + ln (x) - ln (3)

Solution steps

ln (\frac{2 x}{3})

Apply log rule:

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

ln (\frac{2 x}{3}) = ln (2 x) - ln (3)

= ln (2 x) - ln (3)

Apply log rule:

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

ln (2 x) = ln (2) + ln (x)

= ln (2) + ln (x) - ln (3)

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

1000 e^{\frac{4 l n ( 2 )}{3}}

ln (\frac{( t + 5 ) ^{3}}{t ^{4} ( 5 - 1 ) ^{2}})

ln (x^{5}) - ln (x)

- 4 ln (x) + ln (5 y) - ln (4 z)