prove that the following are irrational numbers

1) tan 5

2) log 6 to the base 7

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- Jan 27th 2011, 03:51 AMfxs12irrational numbers
prove that the following are irrational numbers

1) tan 5

2) log 6 to the base 7 - Jan 27th 2011, 04:39 AMSoroban
Hello, fxs12!

Here's the second one . . .

Quote:

. .

Suppose is rational.

Then: .

. . And we have: .

Raise both sides to the power

. . And we have: .

We have a number that has two distinct prime factorizations.

This is contradiction of the Fundamental Theorem of Arithmetic.

Therefore: . is irrational.

- Jan 28th 2011, 12:33 AMmr fantastic
- Jan 28th 2011, 12:49 AMProve It
Is this or ?