Question about logarithmic functions?

Question

How would you use the properties of logarithms to expand this function: ln of 3x^2 divided by (x+1)^5. This should be read as the natural log of three x squared over x+1 to the fifth power. Thanks.

Answer 1

ln( 3x^2/(x+1)^5 = ln(3x^2) - ln(x+1)^5 = ln3 + 2 ln x - 5ln(x+1).

Answer 2

By using the log propertis log AB= log A + log B and
log (A/B)= log A - log B we can write
log (3x^2/(x+1)^5)= log 3+2logx - 5 log (x+1)

Answer 3

ln [(3x^2) / (x+1)^5]

First rule: ln (a/b) = ln a - ln b and ln a*b = ln a + ln b

So,
ln [(3x^2) / (x+1)^5] = ln (3x^2) - ln (x+1)^5
=ln 3 + ln x^2 - ln (x+1)^5

Second rule: ln a^c = c*ln a

ln 3 + ln x^2 - ln (x+1)^5
=ln 3 + 2*ln x - 5*ln(x+1)

Answer 4

The basic properties that you need to know to solve this for yourself are:

ln( a b) = ln(a) + ln(b)

ln( x ^ y) = y ln( x)

Answer 5

ln((3x^2)/((x + 1)^5))
ln(3x^2) - ln((x + 1)^5)
ln(3x^2) - 5ln(x + 1)
ln(3) + ln(x^2) - 5ln(x + 1)
ln(3) + 2ln(x) - 5ln(x + 1)