## Exponential and Logarithmic Functions Review

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AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

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Command ?Terms ? These ?command ?terms ?indicate ?the ?depth ?of ?treatment ?required ?for ?a ?given ?assessment ?statement. ?These ?command ?terms ?will ?be ?used ?in ?examination ?questions, ?so ?it ?is ?important ?that ?students ?are ?familiar ?with ?the ?following ?definitions. ?

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to solve exponential equations without logarithms, you need to have equations with comparable exponential expressions on either side of the "equals" sign, so you can compare the powers and solve. In other words, you have to have "(some base) to (some power) equals (the same base) to (some other power)", where you set the two powers equal to each other, and solve the resulting equation. For example:
Solve 5x = 53.
Since the bases ("5" in each case) are the same, then the only way the two expressions could be equal is for the powers also to be the same. That is:
x = 3

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base of log is 10
base of natural log (ln) is e

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Since hyperbolic functions are defined in terms of exponential functions, it is expected that their inverses can be expressed in the inverse of their exponential functions: Inverse Hyperbolic Functions in terms of logarithms

7inver1,7inver2,7inver3,7inver4,7inver5,7inver6,7inver7,7inver8,7inver9,7inver10,7inver11,7inver12

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