SOLUTION: If 2^a = 3, 3^b = 2, find 1/(a+1) + 1/(b+1)

Question 1209572: If 2^a = 3, 3^b = 2,
find 1/(a+1) + 1/(b+1)

Found 3 solutions by ikleyn, greenestamps, mccravyedwin:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
If 2^a = 3, 3^b = 2,
find 1/(a+1) + 1/(b+1)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If 2^a = 3 and 3^b = 2, then 2^(ab) = (2^a)^b = 3^b = 2, which implies ab = 1. Now, + = = = = = = 1. ANSWER. If 2^a = 3, 3^b = 2, then + = 1.

At this point, the problem is solved to the end.

The answer is really unexpected.

True / good entertainment problem with the unexpected end.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here is a very different solution. More work than the solution provided by tutor @ikleyn... but it gives the student a lot of practice with rules of logarithms.

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ANSWER: 1

Answer by mccravyedwin(407)   (Show Source): You can put this solution on YOUR website!

That's a clever way for it avoids logarithms. But I think this student is studying solving exponential equations by taking natural logs of both sides. So I think the student would do it this way: Edwin

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