simplify ln(7x^3y)

Solution

simplify

ln (7 x^{3} y)

ln (7) + 3 ln (x) + ln (y)

Solution steps

ln (7 x^{3} y)

Apply log rule:

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

ln (7 x^{3} y) = ln (7) + ln (x^{3}) + ln (y)

= ln (7) + ln (x^{3}) + ln (y)

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= ln (7) + 3 ln (x) + ln (y)

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

2 lo g_{10} (x) - 5 lo g_{10} (y)

lo g_{3} (x) - lo g_{9} (4 x)

4 ln (2 x^{3 y})

ln (\frac{4 x}{3 + x})