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# Quick proof of log rule using integrals watch

1. Using the definition of the natural log function (integral of 1/t dt from 1 to x), how would I prove ln(x) + ln(y) = ln(xy)
2. Note that . Can you think of a useful substitution to make for the second integral? [Hint: compare its limits with the limits you want, namely 1 and y.]
3. Sorry, I'm being really dim today and can't spot it. I want x=1 for the limits on the integral furthest to the right so I get 1 and y?
4. (Original post by blap)
Sorry, I'm being really dim today and can't spot it. I want x=1 for the limits on the integral furthest to the right so I get 1 and y?
Put (which is valid since ).
5. Thanks, it's so obvious! I think I was getting confused with the x and y being together, and so not thinking to introduce some other variable.

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