Question

How do you condense `1/4log_3a+5log_3b-log_3c`?

Answer 1

see below

Explanation:

Use the following Properties of Logarithim:

1. `log_b x^n =n log_b x`

2. `log_b (xy)=log_bx+log_by`

3. `log_b(x/y)=log_bx-log_by`

Hence,

`1/4 log_3 a+5 log_3 b - log_3 c = log_3 a^(1/4)+log_3b^5-log_3 c`

`=log_3 ((a^(1/4) b^5) / c)`

`=log_3 ((root 4 (a) b^5)/c)`