simplify 4x-ln(4x)

Solution

simplify

4 x - ln (4 x)

4 x - 2 ln (2) - ln (x)

Solution steps

4 x - ln (4 x)

Apply log rule:

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

ln (4 x) = ln (4) + ln (x)

= 4 x - (ln (x) + ln (4))

ln (4) = 2 ln (2)

= 4 x - (ln (x) + 2 ln (2))

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

= 4 x - 2 ln (2) - ln (x)

- ln (3 (1 - x))

4 lo g_{10} (2) + 3 lo g_{10} (x)

4 ln (x + 3) - \frac{1}{5} ln (4 x + 7)

2 lo g_{2} (3) - lo g_{2} (5)

lo g_{10} (2) + lo g_{10} (11)