7/8 - logarithms + exponentials Flashcards
1
Q
log ₐn = x
A
a^x = n
2
Q
how to deal with logs
A
- missing power - a to the power of what gives n
- do the same operation to each side - to undo a power do logs - to undo a log do to the power of
3
Q
graph of y = logx
A
reflect exponential graph in the line y = x
root is 1
4
Q
log x + log y
A
= log xy
5
Q
log x - log y
A
= log x/y
6
Q
log x^k
A
= k log x
7
Q
log ₐ1
A
0
8
Q
log ₐa
A
1
9
Q
log (1/x)
A
= log x^-1 = -log x
10
Q
inverse of e^x
A
ln x
11
Q
ln e ^x
A
= x
12
Q
e ^ln x
A
x
13
Q
e
A
- Eulers number
- one of the 5 most fundamental constants in maths
- y = e^x > dy/dx = e^x ( the differentiation of the function is the same as the normal function)
14
Q
if y = e^kx then dy/dx =
A
dy/dx = ke ^kx
15
Q
what key features of the exponential function make them suitable for pop growth
A
- a^x gets a times bigger as x increases by 1
- the rate of increase is proportional to the size of the population at a given moment
