Question

How do you solve `log _2 (x+2) - log _2 (x-5) = 3`?

Answer 1

6

Explanation:

Use, `log_bm-log_bn=log_b(m/n)` and, if `log_b a=c` then `a=b^c`

`log_2 (x+2)-log_2 (x-5)`

`=log_2((x+2)/(x-5))=3`. Inversely,

(x+2)/(x-5)= 2^3=8#. Solving,.

x=6..