Page 9 - Math SL HB Sem 1

IN

I. INDICES

Properties of Integer Indices:

Iror m and n integers and a and b real numbers:
l. at x an = am+n

2. (a''rn u'u
--
3. (ab)*: a.b.

. ( a\'' o-
" l;] =6';b+o

o
5 =_ I . a r 0
(I
I
()
di and da' ; a+o

2. I-OGATTITTIMS TO AT{Y BASE,
x-bY y=log5x

(index fbrrn) (log form)

Properties ol logarithm: rf c b, c, M, and N are positive real numbers, b+ r and p
and x are real numbers,then
l.log6l=0 2. log6b=l 3. log6b":x 4. bro8o,:x, * _-

0

5. log MN=log6M+logbN 6 lo96{ = log 6M - Iog 6 N
6

7. log6fr4r': p log6M
8. logb6M:logsN if and only if M - N
e rog"c= :ej 10. log,U:-l
log, o logb (]

CAUTION (Common errors):
, 'ffi# * ro96 M - ro96 N 2. logs (M+N) +logb M + logb N

3. ( logr M ) I' + p logb M

l-l