simplify ln(3/(2x))

Solution

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= ln (3) - ln (2 x)

Apply log rule:

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

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

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

- (ln (2) + ln (x)) : - ln (2) - ln (x)

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

200 ln (\frac{400}{500 - 490})

2^{\frac{l n ( 3 )}{l n ( 2 ) - l n ( 3 )}}

6 lo g_{3} (5 x + 2) + 5 lo g_{3} (3 x + 6)

e^{(x - 2 y)} - ln (2 x^{(2)} y)

lo g_{a} (\frac{( 5 ^{2} y )}{- 1 ^{3}})