Use the properties of logarithms to expand this functiion?
ln[ (x^2+1) (x-1) ]
So assuming this is a multiplication problem, I would be using the product rule for expanding logs. I tried applying the product rule but I'm not sure if this is correct or not?
ln(x^2+1)+ln(x-1)
yes, you are correct
log (AB) = logA + logB
Your approach is correct! To expand the given expression using the properties of logarithms, you can indeed apply the product rule. The product rule states that the logarithm of a product is equal to the sum of the logarithms of the individual factors.
So, starting with ln[(x^2+1)(x-1)], you can split it into two separate logarithms using the product rule:
ln[(x^2+1)(x-1)] = ln(x^2+1) + ln(x-1)
By applying the product rule, you correctly separated the expression into the sum of two logarithmic terms. Therefore, ln(x^2+1) + ln(x-1) is the expanded form of the given expression using the properties of logarithms. Well done!