Solve the equation

Question

log₂ 3 + log₂ x = log₂ 5 + log₂(x − 2)

Answer 1

Everything in your problem has a log₂.   That means that we can combine the logs on each side (or condense them).

These are properties listed in your book or in your notes.  Logs that are added can be condensed (or "smashed together") so that the terms inside are added.

log₂ (3*x) = log₂ (5(x-2))

Now because there is a log₂ on both sides, you can cross that off and just deal with the terms inside:

3x = 5(x-2)

Now you have a regular equation to solve.  

Just remember that you must check to make sure that the x-value you find does NOT give you a negative number inside the log - if it does, you have to "throw out" that solution.