Lucky for us, although intimidatingly rapid at first, our villain slows quickly. Rather than increasing its increase-tion with each increase in x and decreasing its decrease-tion with each decrease in x, this fiend would decrease its increase-tion with each increase and increase its decrease-tion with each decrease. (For a less word-ed analysis of this, see "Possibly Dangerous" on the right)
In sneaking a look at the next chapter in your book, you also probably discovered that this anti-exponent-graph is called the Logarithmic Function.
Logarithmic Function:
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Although most commonly written in Logarithmic Form (top), the Logarithmic Function may also disguise itself as its counterpart in Exponential Form (bottom).Both equations are asking what power you must raise a to in order to equal x. Stay informed. Do not become prey to its deception.
Log Graph:
Because the Logarithmic Function is the inverse of the Exponential Function, its domain, range, and asymptotes are switched. Shifting the graph up/down will change the intercept and right/left will change the asymptote and the domain.
Domain: (0,∞)
 |
| Nautilus Shell- the perfect logarithmic spiral |
Vertical Asymptote: x = 0
Intercept: (1,0)
Log Properties:
Inverse Properties:
One -to- One Property:
The Natural Log: e
Just as it exists with exponents, the irrational number e also comes into play with logarithms.
It follows the same rules as any other logarithm but it is often written
.
Log Doodles: http://www.youtube.com/watch?v=ahXIMUkSXX0
Thats just about all there is to say about Logarithms until next section..
'Log'ing off.... Olivia Miller
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