Question

How do you express `\frac { 1} { 2} \log _ { c } x + 3\log _ { c } y - 5\log _ { c } x` as a single logarithm?

Answer 1

`log_c (y^3sqrt(x^-9))`

Explanation:

`nlog_ab = log_a b^n`
`log_ab + log_ac = log_a b*c`
`log_ab - log_ac = log_a (b/c)`

`1/2log_cx +3log_cy - 5log_cx = log_cx^(1/2) + log_c y^3 - log_c x^5 =`

`= log_c ((x^(1/2)y^3)/x^5) = log_c (x^(-9/2)y^3) = log_c (y^3sqrt(x^-9))`