202 7 8 logarithm a y = y a y log a a log a y = log a = ep a y a > 0, a > 0 log 5 25 log 5 25 y y = log 5 25 25 = 5 y 25 25 = 5 3 y = 3 log 5 25 = 3
2 log 3 9 log 0 0 a log 9 3 2 log 3 9 y 3 y = 9 3 2 = 9 y = 2 0 y = 0 a log 0 0 a = a 9 2 = 3 log 9 3 = 2 a 0 = a = a log a a = log a = 0 log a a =. log 3 9 2. log 0 0 a 3. log 8 2 4. log 0 0.0 2
() log a y = log a + log a y (2) log a y = log a log a y (3) log a y = y log a () log a y = log a + log a y log a y u a u = y log a = v log a y = w a v = a w = y a u = y y a u = y = a v a w = a v+w u = v + w log a y = log a + log a y a n a m = a n+m 2 (2) log a y = log a log a y log a u y au = y log a = v log a y = w a v = a w = y a u = y y a u = y = av a w = av w 3
u = v w log = log a y a log a a n a m = an a m 3 (3) log a y = y log a log a u a u = y (a u ) y = y (a u ) y = a uy a uy = y a log a y = uy = y log a (a n ) m = a nm 2. log 2 4 + log 2 24 2. log 3 32 log 3 64 0 e (natural logarithm) 4
log e log ln log a = log b log b a log a = log a b log b log a = log a a b log a = log b log b a u u = log a a u = b log b a u = log b log a y = y log a u log b a = log b log a = u = log b log b a 3 log 2 3 log 3 6 2 (logarithm fuction) f : X Y f. Y X 2. f() = y f (y) = 5
y y = log 2 0 : a log a y = log a = ep a y log a = 0, log a a = y > 0 > 0 log a a > y = log 2 y = log 2 (+) > y y = log a ( p)+q y = log a p y q e e y = log e = log ep ep log = log ep 45 6
y y = log 2 ( + ) 0 2: 2 y y = log e 0 3: 7
y y = ep y = log y = 0 4: 8
3 2 ( + ) = + = log (+ ) 3 0 % 3 0 % 0000 = log (+0.0) 00000 = log.0..0 = log.0. = log 0. log 0.0 Ecel LOG0 = log 0. log 0.0 = 0.04392685 = 9.57859404 0 0.00432374 0 4 0.% 0 log 0.00 = 0.00043 0 0 00 0. 2 Ecel LN 9
2 r 00% 2 = log 2 log( + r) 4 0.5% 2 4 log 2 = log( + 0.00) = log 2 log.00 = 0.000434077 = 38.975726 39 0.693478 2 72 72 2 = 72 72 = 72 0.5 = 44 44 39 r 00% 2 = log 2 log( + r) 0
y y = y = log( + ) 0 5: log( + r) r y = log( + ) = 0 y = = log 2 log( + r) log 2 r 72 00 00 log 2 r( ) log 2 0.693 69.3 72 ( ) 5 2 72 () 2% (2) 3% (3) 8% (4) 2%