prove that the following are irrational numbers
1) tan 5
2) log 6 to the base 7
Hello, fxs12!
Here's the second one . . .
. .
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.