Write 3 log x − 4 log ( x^2 + 1 ) + 4 log ( x − 1 ) as a single logarithm. Assume all arguments represent positive numbers.

Answer 1

Using the log power property, we can make the n umbers in front of the logs into exponents

log x³ - log(x² + 1)4 + log (x-1)⁴

Next we use the log quotient and product properties to combine the three log terms into 1.

log (x³(x - 1)⁴)/(x² + 1)⁴