write
x^2-11/5 log(2 x-1)+11/5 log(x-2)+ c
as a single log
im not sure how to change the brackets
To rewrite the expression as a single logarithm, we can make use of the properties of logarithms.
First, let's simplify the expression:
x^2 - (11/5) log(2x-1) + (11/5) log(x-2) + c
Now, let's apply the logarithmic properties:
1. Product rule: log(a) + log(b) = log(ab)
2. Quotient rule: log(a) - log(b) = log(a/b)
3. Power rule: n * log(b) = log(b^n)
Using these rules, we can rewrite the expression as follows:
x^2 + log((x-2)^(11/5) / (2x-1)^(11/5)) + c
Therefore, the expression can be written as a single logarithm:
log((x-2)^(11/5) / (2x-1)^(11/5)) + x^2 + c