Use the properties of logarithms to expand the expression. ln y(y+1)^5, I keep coming up with the same answer which is wrong.
y^5ln(y)+5y^4ln(y)+10y^3ln(y)+10y^2ln(y)+ln(y)
Yep, it is wrong.
ln y(y+1)^5
lny + 5ln(y+1). so I don't know where that is in, or has to do with this. y^5ln(y)+5y^4ln(y)+10y^3ln(y)+10y^2ln(y)+ln(y) ...
Are you treating this as (Y+1)^5 *lny ? I don't think that is what was intended, my guess the intended expansion is
ln{ y(y+1)^5} which is
lny + 5ln(y+1)
ln(y) + 5 ln(y+1)
To expand the expression ln y(y+1)^5 using the properties of logarithms, you can use the rule that states ln(xy) = ln(x) + ln(y). In this case, we have ln y(y+1)^5.
First, apply the rule by writing it as a sum:
ln y + ln(y+1)^5
Next, we can expand ln(y+1)^5 using the rule that states ln(a^n) = n ln(a). In this case, we have ln(y+1)^5.
Using the rule, we can write it as:
ln y + 5 ln(y+1)
Now we have the expanded expression. It is important to note that you obtained the same answer because ln(y+1) does not contain any y terms, so when you expanded it, you only got ln(y) terms.