simplify x^2-ln(4x)

Solution

simplify

x^{2} - ln (4 x)

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

Solution steps

x^{2} - 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)

= x^{2} - (ln (x) + ln (4))

ln (4) = 2 ln (2)

= x^{2} - (ln (x) + 2 ln (2))

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

= x^{2} - 2 ln (2) - ln (x)

lo g_{3} (x) - lo g_{3} (0.5)

ln (x - 6) - ln (x - 2) + 10 ln (x)

6 ln (\frac{1}{2})

ln (\frac{16}{15})

ln (64) + ln (7) - 5 ln (2)