How do you solve log_2 (3x)-log_2 7=3?

1 Answer
Jul 8, 2016

Use a property of logs to simplify and solve an algebraic equation to get x=56/3.

Explanation:

Begin by simplifying log_2 3x-log_2 7 using the following property of logs:
loga-logb=log(a/b)
Note that this property works with logs of every base, including 2.

Therefore, log_2 3x-log_2 7 becomes log_2 ((3x)/7). The problem now reads:
log_2 ((3x)/7)=3

We want to get rid of the logarithm, and we do that by raising both sides to the power of 2:
log_2 ((3x)/7)=3
->2^(log_2 ((3x)/7))=2^3
->(3x)/7=8

Now we just have to solve this equation for x:
(3x)/7=8
->3x=56
->x=56/3

Since this fraction cannot be simplified further, it is our final answer.