Question

Prove that \(\log _a a=1\)

Answer 1

To prove that \(\log_a a = 1\), we can use the definition of logarithms. A logarithm with base a is defined as the exponent to which a must be raised to give the number x.

Mathematically, if \(y = log_a x\), then \(a^y = x\).

So in this case, if we set \(x = a\), we have: \(a^{\log_a a} = a\)

Because a raised to the power of \(\log_a a\) is equal to \(a\), then \(\log_a a = 1\)