13 Working with other Bases

13 Working with other Bases - Next: Integrals and the...

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Next: Integrals and the Natural Up: Doing that Calc Thing Previous: Differentiating the Natural Log Working with other Bases You can choose almost any number as the base for logarithms and exponentials. Since we have ten fingers we often think of 10 x and the corresponding logarithm function . In the old days, schoolchildren got lots of practice using tables of logarithms with base ten. If we had two fingers we might have used base two. Come to think of it, we do have two arms. Anyway, these days we only use one finger to peck at the keys of a calculator and the function is disappearing from the world. Let's look at the derivatives of b x and . In particular, let's start with 2 x . Now you might be tempted to say You have to learn to control your baser instincts. The power rule doesn't apply when the base is a constant and the exponent is a variable. Instead, the correct answer is: A factor of multiplies the derivative. Why , for goodness sake, you ask?
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13 Working with other Bases - Next: Integrals and the...

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