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What I want to do in this video is prove the change of base formula for logarithms, which tells us-- let me write this-- formula. Which tells us that if I want to figure out the logarithm base a of x, that I can figure this out by taking logarithms with a different base. That this would be equal to the logarithm base b-- so some other base-- base b of x, divided by the logarithm base b of a. And this is a really useful result. If your calculator only has natural logarithm or log base 10, you can now use this to figure out the logarithm using any base. If you want to figure out the log base 2-- let me make it clear. If you want to figure out the logarithm base, letamp;#39;s say, base 3 of, letamp;#39;s say, 25, you can use your calculator either using log base 10 or log base 2. So you could say that this is going to be equal to log base 10 of 25-- and most calculators have a button for that-- divided by log base 10 of 3. So this is an application of the change of base formula. But let