1

4
xy 2 = 16
From x
y 1
log 10
1
x y 10
x y
10 …………….(i)
xy 16 …………………(ii)
From (i)
x 10 y
Substituting for x in equation (ii)
10
y y
10 y y 2 16
y
y
2
2
16
10
y 16
0
10
y 16
0
10
y
10
10
2
10 6
2
16
or
2
2
10
4 116
2 1
100 64
2
36
4
2
= 8 or 2
When y = 8, x = 2 from x = 10 – y
y = 2, x = 8
Example 5 Solve the equation
3
Solution. x 1
3x
2 22
22
3 x
and 3
x
x2 2
3 3
3 x 2
3 3 x
2 2
2
3x
3
x
2
3
2
2
3 x 1 2
x
3x
2
2
3
log
10 log
x
10
3 2
3x
log 10 2 xlog
10 3 2log 10 3 log 10 2
0.3010
x0.4771
20.4771
0. 3010
3x
0.9030
x 0.4771 x 0.9542 0.3010
3
0.4260
x 0.6532
x 1.5333
3 x 1 2
3
x
3x
1
10 2
x
log 10 3
2
3x
1
log 10 2 x 2 log 10
Alternative 1 2
log
3
3x
1log
10 2 x
2log
10 3 0
3x
1 0.3010 x
20.4771
0
0.9030
x 0.3010 0.4771 x 0.9542 0
0.426
x 0.6532
x 1.5333
Example 6.Find the values of x and y if
x4y
5 5
0
and 3
5x2y
3
x4
y
Solution.From 5 5
sides
0
2
We have x
ylog
5 0log 5
4 5 5
taking log
5
on both
x 4y
0 ………………………….(i)
5x2y
2
And from 3 3 taking log
3
on both
sides
5x
2ylog
3
3 2log
3
3
5x
2y
2…………………..(ii)
From i – ii, x + 4y = 0
10x + 4y = - 4
- 9x 4
- 4
x
9
x
From i, y
4
4
y 4
9
1
9
Exercise 1(c)
1. Solve the simultaneous equations
1
log x y and 1
log 5 x log y 5
2
2. Solve for z in the equation
log 46
z log 2 z
3. Solve for x in equations
(i) log 5 3log 5 x 2
x .
(ii) log 10 x log x 100 3