8/2/2019 log_typ13

1/1

e:

+

+

11lim =2,7182818284590452353602874713527 = e

f(x) = x R , > 0.

0 < < 1 . > 1 .

= 1 .

R (0 , + ).

f(x) = ex

x R .

f(x) = logx , ( > 0 1) x > 0

: 0 < < 1 .

> 1 .

(0 , + ) (- , + ) = R.

logx = y y= x , x > 0 yR.

f(x)= lnx (0 , + )

(- , + ) =R.

lnx , x > 0 ex

, x R.

lnx = y ey= x , x > 0 yR.

a

ln xlog x

lna= , x x lne =

1. log1 = 0

2. log = 1

3. logx= x

4.log x

x =

5. logxk

= k logx

6. log(x y) = logx + logy

7.x

log log x log yy

=

x, y > 0

1. ln1 = 0

2. lne = 1

3. lnex= x

4. elnx = x

5. lnxk

= k lnx

6. ln(x y) = lnx + lny

7.x

ln ln x ln yy

=

x, y > 0