Logarithm Base Changing Formula Proof

In a logarithmic expression, it is possible to change base using algebraic manipulation.  For example, we can change to . In this post, we are going to prove why it is possible to do such algebraic manipulation. The change of base above can be generalized as . Theorem . Proof If we let , then […]
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Year 2015 in Review – Complete List of Posts

It’s the end of the year again, so let’s look at what we have learned so far in 2015. Below is the complete list of posts of mathematical proofs this year. Enjoy learning! Year 2015 in Review – Complete List of Posts Absolute Value Proofs: Products and Quotients Proof of the Converse of the Pythagorean […]
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Proof that the nth root of a times nth root of b is equal to nth root of ab

Consider the following multiplications. . Also . Try also several calculations like these and observe what happens. From these calculations, we can observe that and or, in general . We now, prove our conjecture. Theorem: Proof If we multiply the expression on the left hand side by itself n times, we have . On the […]
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