simplify ln^2(4x)

Solution

simplify

ln^{2} (4 x)

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

Solution steps

ln^{2} (4 x)

Apply log rule:

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

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

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

ln^{2} (4) = 4 ln^{2} (2)

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

lo g_{2} (x^{2}) + lo g_{2} (x - 1) - 4

(- \frac{6}{10}) lo g_{2} (\frac{6}{10}) - (\frac{4}{10}) lo g_{2} (\frac{4}{10})

- (\frac{2}{6}) lo g_{2} (\frac{2}{6}) - (\frac{4}{6}) lo g_{2} (\frac{4}{6})

lo g_{10} (x) - 5 lo g_{10} (y) + 8 lo g_{10} (z)

lo g_{7} (6) + lo g_{7} (3) - lo g_{7} (2)