Rewrite the expression 3log x 5logx212logx1 as a single loga

Rewrite the expression 3log x -5log(x^2+1)+2log(x-1) as a single logarithm log A. then the function A=

Solution

We will use the following log operations rules:

1) log_b(mn) = log_b(m) + log_b(n)

2) log_b(^m/_n) = log_b(m) – log_b(n)

3) log_b(mⁿ) = n · log_b(m)

Then, 3log x – 5 log( x² + 1) + 2log ( x – 1) = logx³ + log ( x -1)² - log (x² + 1)⁵ = log [x³( x - 1)² / (x² + 1)⁵ ]

Thus A = [x³( x - 1)² / (x² + 1)⁵ ]