simplify ln(x^3y)

Solution

simplify

ln (x^{3} y)

3 ln (x) + ln (y)

Solution steps

ln (x^{3} y)

Apply log rule:

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

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

= 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)

= 3 ln (x) + ln (y)

0.0259 \cdot ln (\frac{2.8 \cdot 1 0 ^{19}}{7 \cdot 1 0 ^{15}})

93 + 10 lo g_{10} (5) - 40 lo g_{10} (2)

2 [ln (x + 3) + ln (x) - ln (x^{2} - 1)]

lo g_{4} ((m^{2} n^{3})^{5})

ln (\frac{10}{1})