simplify ln(4x^2)

Solution

simplify

ln (4 x^{2})

2 ln (2) + 2 ln (x)

Solution steps

ln (4 x^{2})

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (4) + 2 ln (x)

ln (4) = 2 ln (2)

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

lo g_{x} (a) - lo g_{x} (b)

ln (\frac{r}{9 s})

ln (\frac{x ^{5}}{y ^{2}})

f (k) = 1 - lo g_{2} (\frac{k - 1}{k})