Page 9 - Math SL HB Sem 1

M trR

I. INDICI'S

Properties of lnteger Indices:

For m and n integers and a and b real numbers:
l. a'x an: am+n

2. (a'")" = an r
3. ( a b;' = um 6'

a a^
i ).
4 =r- ; b*o

a I
-5 =- : a + 0
a' o
I
v
6. a =di ana "f; ; a*0
\JA

2. LOGARITHMS TO ANY BASE
x=bY y=lo96x

(index forrn) (log form)

Properties of logarithm: lf a, b, c, M, and N are positive real numbers, b+ I and p
and x are real numbers,then
l.log6l:0 2. log6S=l 3. lo96b'=x 4. b losb. y,X

0

5. logs MN=log6M+logbN b. togb M =log5M log6N
-
7. logsMP:plog6M :
8. l<.rg b5M log 5 N if and only if M = N
: f
e. rog, c f"t 10. log,b:- L
log^ a
togh a
CAUTION (Com mon errors):
, 'ff# * ro96 M - rogs N 2. lo96 (M+N) +logb M + Iogb N

3. (loghM)r + plog6M

t-t