simplify ln(3x^5y)

Solution

simplify

ln (3 x^{5} y)

ln (3) + 5 ln (x) + ln (y)

Solution steps

ln (3 x^{5} y)

Apply log rule:

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

ln (3 x^{5} y) = ln (3) + ln (x^{5}) + ln (y)

= ln (3) + ln (x^{5}) + ln (y)

Apply log rule:

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

ln (x^{5}) = 5 ln (x)

= ln (3) + 5 ln (x) + ln (y)

\frac{1}{5} x^{5} (3 ln (2) + 2 ln (x))

ln (\frac{393}{373})

\frac{1}{2} ln ∣ 2 (10) + 1 ∣ + 2 ln ∣ 10 - 1 ∣

0.0591 \cdot ln (\frac{0.001}{0.1})

ln (5.5 \cdot 1 0^{- 15})