simplify ln(3x^4y)

Solution

simplify

ln (3 x^{4} y)

ln (3) + 4 ln (x) + ln (y)

Solution steps

ln (3 x^{4} y)

Apply log rule:

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

ln (3 x^{4} y) = ln (3) + ln (x^{4}) + ln (y)

= ln (3) + ln (x^{4}) + ln (y)

Apply log rule:

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

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

= ln (3) + 4 ln (x) + ln (y)

ln (x) + 4 ln (2 - \frac{y}{x})

2 lo g_{10} (x + 3) - 3 lo g_{10} (x)

ln (\frac{3 x ^{5}}{y})

- lo g_{10} (5.8 \cdot 1 0^{- 3})

ln (9) + \frac{1}{2} ln (x + 4) - 2 ln (1 + x)