1

1
t log x 16
2
1
log x 8 log x 16 1
2
1
log 8 log 16 2
x x 1
log
log
log
x
x
x
8 log
x
8
1
4
2 1
2 x x
x 2
1
4 1
Example 4 Solve the equation
2 x 5
4.381 8. 032
x
Solution
2 5
To solve equation x
4.381
x 8. 032
2
x 5
log 10 4.381 log 108.
032 x
2x
5log
10 4.381 xlog
10 8. 032
2x
50.641573
x0.904824
1.28314x-3.207865=0.904824x
0.378322
x 3.207865
x 8.4779192
x 8.5
3
10 10
Example 5 log x 8
Solution
3
10 log 10 x 8
8
log 10 x 0.008
3
10
0.008
x 10 = 1.0186
Exercise 1(e)
1. Solve simultaneous equations
9
log 25 xy and log 5 x 10
log 5 y
2
3
2. Given that y log a x and z log x a .
Show that zy=3, hence find the values of
y and z if
log 3log
a
x
log log
a log 27
a
a
2
2
3. Solve the equation log 4x
log x
4. Solve
i)
x
a
25 5
3
2
x 1
ln
log e log 5
ln x
log 10e
10
10
2
ii ) log 5 xlog
5(
) 1
0
x
5. Solve the simultaneous equations
2 1
log 9xy
and log 3 x log
3 y 3
2
log 4 log 2 x log 2 log 4 x
7. Solve for x in the equation
log 14 x log 7 4x
8. Solve the simultaneous equations
log y 2log
y log
30
x
6. Solve for x if
x 1 and 0
2x
1
x
9. Solve equation 5 4 215
10. Solve the following simultaneous
equations
x
y
2 y
i) 2 4 12 and32
22
16
x
y
ii) 2 3 5 and 2
3
23
x
y
x
x 3
y2
x 2 y
2
iii) 2 3 44 and 2 3 221
iv)log 4 x 2 – 6 log x 4 = 1
1.36 Proof of identities involving
logarithm
Example 1 Given that log 4 p 2log 4 q 2
Show that pq = 16.
Hence solve for p and q in simultaneous
equation
log 10 p q 1
And log 2 p 2log 4 q 4
Solution:
log 4 p 2log 16 q 2
*******************************
Side work;
Let log 16 q t