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welcome to our lecture online in this video weamp;#39;re going to show you the proof of this equation that we can actually change from one base to another and just so that we know the rules of exponentials and logarithms that the base e raised to the natural log of x is simply x and that a raised to the log base a of x equals x this is essentially the same thing because this could be e the log base e of x and so this would be e raised to the log base e of x is equal to x so once we realize that we could then look at this equation and weamp;#39;re going to start with that a raised to the log of a of x equals x essentially x equals x thatamp;#39;s what this equation is saying so we know that to be true now weamp;#39;re going to take the log base b of both sides so we take the log of base b of a raised to the log base a of x and that therefore must equal the log base b of x so all weamp;#39;ve done is on the left side weamp;#39;ve taken the log base b of the left side equals the log
