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exponents & logarithms

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Exponents & Logarithms
Definition :
ab  c

log a c  b
a
: base
a : base ; a  0, a  1
b
: exponent
b : logarithm
ab : power
c
: argument ; c > 0
Properties of Exponent :
Properties of Logarithms :
1. x m  x n  x m n
1. 10 y  x  y  log x
2. x m  x n  x mn
2. log10x  x
3.
 x  y
m
 xm  ym
3. log a b 
log c b
log c a
m
x
xm
4.    m
y
 y
5.
x 
m
6. x
m
n
n
4. loga  xy   loga x  loga y
 
 x mn  x nm  x n
 n xm 
7. x  m 
 x
n
m
m
1
xm
x
5. log a    log a x  log a y
 y
6. log a  x n   n  log a x
7. log x  c  logb x ; c is constant
8. log a b 
8. x0  1 ; x  0
9. x1  x
1
log b a
9. log a b  logb c  log a c
10. log a b  logb c  logc d  log a d
Additional Properties :
1.
n
log am b n    log a b
 
m
2.
a log a b  b
 
log
3.
a
 am 
bn
11. log bn x 
 
1
 log b x
n
12. log bn x n  log b x
 
1
13. log  1     log b x
  x
b
b
n
m
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