Question

How do you simplify `log_ax - log_a9 - log_a(x^2+1) + log_a5`?

Answer 1

`log_a((5x)/(9(x^2+1)))`

Explanation:

Using the following `color(blue)" laws of logarithms "`

`• logx + logy hArr log(xy)`

`• logx - logy hArr log(x/y)`

rewriting the above expression as follows:

`log_a x + log_a 5 -(log_a 9 + log_a(x^2+1))`

`rArr log_a(5x) - ( log_a (9(x^2+1))`

`= log_a ((5x)/(9(x^2+1)))`