Page 34 - mathsvol1ch1to3ans

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log x log y log z
10. If = = , then prove that xyz = 1.
y − z z − x x − y

log x log y log z
Solution: Let = = = log k.
y − z z − x x − y
log x = k(y − z) log y = k(z − x) log z = k(x − y)

log xyz = log x + log y + log z

= k(y − z) + k(z − x) + k(x − y)
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= 0
xyz = 1

11. Solve log x − 3 log 1 x = 6.
2
2
Solution: The given expression can be rewritten as
1 3
− = 6
log 2 log x 1
x
1 3 2
+ = 6
log 2 log 2
x x
4
= 6
log 2
x
4 log x = 6
2
3
log x =
2
2
3
√
x = 22 = 2 2

2
12. Solve log 5−x (x − 6x + 65) = 2.
Solution:Rewriting in exponential form we have

2
(5 − x) 2 = x − 6x + 65
2
2
25 + x − 10x = x − 6x + 65
4x = −40

x = −10
Exercise 3.1:

1. Identify the quadrant in which an angle of each given measure lies
◦
(i) 25 ◦ − first quadrant (ii) 825 ◦ − second quadrant (iii) −55 − fourth quadrant
◦
◦
(iv) 328 − fourth quadrant (v) −230 − second quadrant
◦
2. For each given angle, find a coterminal angle with measure of θ such that 0 ≤ θ < 360 ◦
◦
◦
◦
(i) 395 ◦ ≡ 35 (ii) 525 ◦ ≡ 165 (iii) 1150 ≡ 70 ◦
◦
◦
◦
(iv) −270 ≡ 90 (v) −450 ≡ 270 ◦