1310-Notes-Sec-53-filled

1310-Notes-Sec-53-filled - Math 1310 Section 5.3 Logarithms...

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Math 1310 Section 5.3 Logarithms Earlier, you learned to find the inverse of a function. Let’s apply the same method from Chapter 3 to help find the inverse of an exponential function. If x x f 3 ) ( = , rewrite the function as x y 3 = . Interchange x and y : y x 3 = . Now we need to solve the equation for y . Hmmmmm. We need something to help us out here. We want to be able to choose values for the independent variable, x , and then easily calculate y and from this form of the equation, there is no such easy calculation. Enter logarithms. For 1 , 0 a a , the logarithm with base a , written x a log is the exponent to which a must be raised in order to give x . There are two very special logs: The common logarithm is the logarithm with base 10. We denote this as x x log log 10 = . The natural logarithm is the logarithm with base e . We denote this as x x e ln log = You will find both of these logarithms on a scientific calculator. Note:
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1310-Notes-Sec-53-filled - Math 1310 Section 5.3 Logarithms...

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