untitled

or
4 2 22 4
a ( 20 ) {( 25 )} ( 2 5 )

or
4 4
a ( 25 )
?a 25
? the base is 2 5
Example 9. Find the value of x:
(a)log 10 x  2 (b) logx 324 4
Solution :

(a) 2log 10 x 

001

001

100

1

10

1

10

2

2

? ˜

? ˜

? 

x

x

x

(b)logx 324 4

3 2.

or ( 3 2 )

3 2 3 ( 2 )

324 3 3 3 3 2 2

4 4

4 2 4 4

4

?

u u

? u u u u u

x

x

x

Example 10. Prove that, 3 log 102 log 105 log 1040

Solution: Left hand side = 3 log 102 log 105

log 1023 log 105 ,[logaMr rlogaM]

log 108 log 105

log 10 ( 8 u 5 ),[loga(MN) logaMlogaN]

log 1040 = Right hand side (proved).

Example 11. Simplify :
log 12

log 27 log 8 log 1000

10

10 10 10

˜

 

Solution :
log 12

log 27 log 8 log 1000

10

10 10 10

˜

 

10

12

log

log ( 3 ) log 2 log ( 10 )

10

2

1

3

10

3

(^210)
1
3
10  
log 12 log 10
log 3 log 2 log 10
10 10
2
3
10
3
10
2
3
10

 
log ( 3 2 ) log 10
log 10
2
3
log 3 3 log 2
2
3
10
2
10
10 10 10
u 
 
ȏ‹ˆax bxǡa b]