Question

How do you condense `1/3ln x + ln y`?

Answer 1

`1/3lnx+lny=ln(yroot(3)x)`

Explanation:

We can condense using identities

`log_ap_1+log_ap_2+log_ap_3+..+log_ap_n=log_a(p_1*p_2*p_3*...*p_n)`

and `nlog_ap=log_ap^n` and

`1/mlog_ap=log_ap^(1/m)=log_aroot(m)p`

Using these `1/3lnx+lny=lnroot(3)x+lny=ln(yroot(3)x)`