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logarithms and e
chapter 14 - exponentials and logarithms
| Term | Definition |
|---|---|
| exponential functions | y = a^x, limiting at (0,infinity) as x approaches (-infinity, infinity) and a > 1 (0<a<1 flips this) |
| e spec definition | an irrational number such that f(x) = f’(x) = e^x |
| derivative of e^kx | k*e^kx |
| models using exponential functions | when the rate at which a variable changes is based on the current value of the variable itself |
| logarithms | log base a (n) = x is identical to a^x = n (as long as a =/= 1 and n>0) |
| special logs in the a-level spec | log = log base 10 ln = log base e |
| laws of logarithms (if the bases are the same) | log (a) + log (b) = log (ab) log (a) - log (b) = log (a/b) log (a^b) = b*log (a) log (1) = 0 log base a (a) = 1 |
| logarithm definition | the inverse of exponentiation ie when an exponential function is reflected along the line y=x |
| logarithms of exponential graphs | form a linear equation in terms of logarithms |
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