What is x if #log_2(3-x) + log_2 (2-x) = log_2 (1-x)#?
No solution in
First, use the logarithm rule:
Here, this means that you can transform your equation as follows:
At this point, as your logarithm basis is
Please beware that you can't do such a thing when there is still a sum of logarithms like in the beginning.
So, now you have:
This is a regular quadratic equation which you can solve in several different ways.
This one sadly doesn't have a solution for real numbers.
I totally concur that there is no solution for
If on the other hand we look at the potential of
Using standard form
We then we end up with:
My understanding implies that the question given needs to be checked.
Log addition is the consequence of multiplication of the source numbers/variables.
The equals sign is a
Both sides of the equals sign are to log base 2. Suppose we had some random value of say
Solution to this problem:
Take antilogs of both sides giving in the question implies:
This I believe to be