simplify ln(4x^2y)

Solution

simplify

ln (4 x^{2} y)

2 ln (2) + 2 ln (x) + ln (y)

Solution steps

ln (4 x^{2} y)

Apply log rule:

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

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

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

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 (y)

ln (4) = 2 ln (2)

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

lo g_{10} (x) + \frac{1}{6} lo g_{10} (y)

- 0.2 lo g_{2} (0.2) - 0.8 lo g_{2} (0.8)

ln (4 \cdot cos (x))

3156659.5 \cdot ln (\frac{6.8}{1.2})

ln (\frac{( 2 x + 1 ) ^{5}}{x ^{2} + 1})