# What is x if #log_2(3-x) + log_2 (2-x) = log_2 (1-x)#?

##### 2 Answers

No solution in

Solutions in

#### Explanation:

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.

Tony B:

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.

#### Explanation:

Pre-amble

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

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Solution to this problem:

Take antilogs of both sides giving in the question implies:

This I believe to be

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