Prove the change of base formula for logarithms. That is, prove that log_a (x) = log_b (x) / log_b (a).
Firstly, recall the definition of a logarithm: if y = loga(x), then this means that y is the power you have to raise a to, to get x, that is ay = x.Now, we want to introduce a new base, b. Let's take log to base b of both sides of the above equation. We get logb(ay) = logb(x). But remember our rules of logarithms -- we know that ylogb(a) = logb(ay), so we get that ylogb(a) = logb(x).Lastly, divide both sides by logb(a), to obtain: y = logb(x)/logb(a). Aha! Remember we started off by saying that y = loga(x). Therefore, loga(x) = logb(x)/logb(a), and our proof is complete!
TH
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