Logs

Q:  Solve:  log(5x − 7) − log(4x − 5) = 0

A:  Rearrange by adding the log(4x – 5) to the other side to get:

log(5x – 7) = log(4x – 5)

Now, since we have log(something) = log(something), we can get rid of the “log” part…

So,

5x – 7 = 4x – 5

Now solve!

x – 7 = -5

x = 2

Whenever you get a solution with logs, you should plug it back into the original problem to make sure we have no errors.  What would an error be??? You cannot take the log of 0 or a negative number, so plug your answer in to make sure nothing is 0 or negative like so:

log(5x − 7) − log(4x − 5) = 0

Plug in x = 2:

log(5(2) − 7) − log(4(2) − 5) = 0

log(3) – log(3) = 0

Good, all the values inside the logs are positive numbers.  So, x = 2 is a solution!

Note:  I did not explain what a “log” is or give complete undrestanding on how to manipulate one, I just should how to do this specific problem… If you are stuck on the concept of “logs”, let me know… I can explain them in detail (in language that is easy to understand)