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Introduction to Logarithms
1.
Logarithms
2.
?? ?? LOGARITHM ?? ??
3.
Inverse Functions • Original
function: y = kx => f (x) = kx • Inverse function: x x -1 x = ky => y = => f (x) = k k
4.
Example f (x) =
2x;f -1(x) = x 2
5.
Inverses Invert x g(x) = 2 f
(x) = 2x ( æ xö f g (x) = 2 ç ÷ = x è 2ø ( 2x g f (x) = =x x ) )
6.
y =k Invert y =k x x
=k y Now solve for y. x
7.
??????????? ?????????????
8.
Enter the Logarithm () loga
b = c means a =b c “Jumping Horse Outline”by warszawianka. Found at http://openclipart.org/detail/10712/jumping-horse-outline-bywarszawianka-10712. Public domain.
9.
x =k Solution: y y =
logk x
10.
() loga b =
c a =b c Implications? Graphs of inverse functions reflect over line y = x.
11.
Implications • • • • Increasing Asymptote: y-axis =>
x>0. loga1=0. logaa=1.
12.
Summary Basic relationship: y =
a <=> x = loga y x
13.
Next Yes but so
what?
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