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PROVE THAT log105 is irrational
Let us suppose that the given quantity is a rational number, such that:
Log_10(5) = a/b
Then, we must have: 10^a =5^b
Thus the last digit in the LHS is always 0 and the last digit in the RHS is always 5.
This is a contradiction.
Therefore, our supposition that the given expression was rational is erroneous, and therefore it follows that log _10(5) is always irrational.
Edited on May 6, 2023, 7:26 am
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