Rewrite the expression
2logx−3log(x^2+1)+4log(x−1)
as a single logarithm logA. Then the function
To rewrite the expression 2log(x) - 3log(x^2+1) + 4log(x-1) as a single logarithm, we need to use logarithm properties.
First, let's start by applying the power rule of logarithms, which states that log(basea)(x^b) = b*log(basea)(x).
Using this rule, we can rewrite the expression as:
log(x^2) - log((x^2+1)^3) + log((x-1)^4)
Next, let's apply the quotient rule of logarithms, which states that log(basea)(x) - log(basea)(y) = log(basea)(x/y).
Using this rule to combine the first two terms, we have:
log(x^2 / (x^2+1)^3) + log((x-1)^4)
Finally, let's apply the product rule of logarithms, which states that log(basea)(x) + log(basea)(y) = log(basea)(x*y).
Using this rule, we can combine the last two terms and rewrite the expression as a single logarithm:
log((x^2 / (x^2+1)^3) * (x-1)^4)
So the expression 2log(x) - 3log(x^2+1) + 4log(x-1) can be rewritten as log((x^2 / (x^2+1)^3) * (x-1)^4).
Please note that the function you mentioned at the end of the question is incomplete. If you can provide more details about the function, I would be happy to help you further.