ln x^2(x+1)/x+2

Write in terms of ln(x), ln(x+1), and ln(x+2)

is the correct steps this?
lnx^2 + ln(x+1) - ln(x+2) = 2lnx + ln(x+1) - ln(x+2)

Good job.

To write the expression ln(x^2(x+1)/(x+2)) in terms of ln(x), ln(x+1), and ln(x+2), you can simplify the expression following these steps:

Step 1: Apply the rule of logarithms for division. That is ln(a/b) = ln(a) - ln(b).

ln(x^2(x+1)/(x+2)) becomes ln(x^2) + ln(x+1) - ln(x+2).

Step 2: Apply the power rule of logarithms. The power rule states that ln(a^b) = bln(a).

ln(x^2) becomes 2ln(x).

Now, substituting this back into the expression, we have:

2ln(x) + ln(x+1) - ln(x+2).

So, the correct expression in terms of ln(x), ln(x+1), and ln(x+2) is 2ln(x) + ln(x+1) - ln(x+2).