SOLUTION: Log2 (3^(x) -8)= 2-x

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Question 1146649: Log2 (3^(x) -8)= 2-x
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In general, an equation like this can only be solved approximately, by numerical methods.

However, a bit of studying of this equation can reveal a simple solution.

log%282%2C3%5Ex-8%29+=+2-x --> 2%5E%282-x%29+=+3%5Ex-8

The expression on the left is positive. So if there is a nice whole number solution to the problem, x must be at least 2. So try x=2.

2%5E%282-x%29+=+2%5E%282-2%29+=+2%5E0+=+1
3%5Ex-8+=+3%5E2-8+=+9-8+=+1

ANSWER: x=2