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3 2n 3  18   3  2 n  1
34. (a) Simplify 2 .
 
5 3 n

1

log 8 log 27  2 log 5
(b) Without using the calculator, evaluate 10 10 10 .
3 log 6 log 5

2 10 10


(c) Solve x  5 4x  13.


35. Solve the equation 2log 3 log x 3  3 0.
x

36. Given √ + √3 = 5 where p and q are integers. Find the value of p and q without using a
2+√3
calculator.

37. Solve the equation 9 + 4 = 5(3 ).

38. Solve the equation 4 − 16 = 6(2 )

2
2
39. Show that log ( + √ − 1) + log ( + √ − 1) = 0


2 10
1/3
6
64 p q r


10 2
2
40. (a) Simplify 8 2/3 p q r
4 x  2 y
(b) Solve  1 if xy 
9
3 x



41. Find the values of x which satisfies the equation log (5 x ) log (x  2) 3 log (1 x

)
2
2
2

 
42. Solve the equation:   3 2x 1  3 7 3 x
2
1 1
 11   11  2
2
43. a) Evaluate  3     3   without using calculator


 

 2   2 
1 1
b) Show that   1
log pq log pq
q
p
n
243  3 2n 1
5
n
44. a) Evaluate 9  3 n 1