We can't tell whether you mean the 3's to be the base of the logarithm
like this:
or whether you mean the 3's to be multipliers and the logarithms understood
to be common logs with understood base 10, like this:
If it's the first way then we drop the logs and get this:
If it's the second way then we drop the logs and get this:
But if it's that way we divide both sides by 3 and get
So, luckily here it doesn't matter which you meant but in other
logarithm problems it would make a difference. So be careful.
Get 0 on the right and descending order on the left:
But we must check in the original equation for extraneous solutions.
If it was the first way, we check to see if 5 is a solution:
It looks like it checks but it doesn't because logs cannot be taken of
negative numbers in real number mathematics. So 5 is extraneous.
If it was the first way, we check to see if -3 is a solution:
That checks. So x = -3 is the only solution.
If you meant the other way, it still would be only x = -3.
Edwin
