1. BA101 – index exercise 2
Solve the equations using index method: xii. log 2 6 x log 2 ( x 3) 2 x 6
1
i. 52 n 1
25n 1
125n 1
53n 6
xiii. 125 x 2
x 2
3 25 2 x 4
8n 4
ii. p3 q 2n p 2n
xiv. log 2 (4 x 1) 3 log 2 x x
1
3n 4
2
q
1
iii. 32 m 5 n 10 5
2mn 2
Given that log 7 5 0.83 and log 7 6 0.92 ,find
iv. 32 n (81n 1 )(9 2 3n
) 1
the value of the following without using a
2 3 4 calculator
(a b )
v. a2 i. log 7 30 1.75
(a 3b 6 ) 2
1
82 n 43n ii. log 7 1 0.09
vi. 2 3n
5
2 n 16 2 n
2 Given that log 2 3 1.59 and log 2 5 2.32 ,find
vii. 22 x 4
1 the value of the following without using a
16 x 2
Simplify the logarithmic equations below: calculator
1 1 i. log 2 45 5.50
i. log a 2 log b log c a c 3
3 log
b 2 ii. log 2 0.6 0.73
ii. 4 log x 2 log y log x 4 log z log x y 3 2
Given that log2 a = m and log 2 b = n. Write
z4
2a
iii. 3 log b 4 log a 2 log z a4 log2 in terms of m and n. 1 m n
log
b3 z 2
b
Find the value of x:
Given that log 3 2 m and log 3 5 n, write
i. log 50 log x 2 log(2 x 1) x
2
3 log1.2 in terms of m and n 1 m n
ii. log 3 (3 2 x) 3 x 12
iii. log 5 (5 x 4) 2 log 5 3 log 5 4 x 8
iv. log x 8 5 log x 4 x 2
If log 5 3 0.682 ,find the value of this equation:
x 2x
v. 2 4 16 x
4
3 4 2
5 log 5 2 log 5 log 5 0.318
1 8 5 5
vi. 3x 1
27 x x
3
9 4
1
vii. 128 x 7
2x
viii. 27 x 9 x
2
3
ix. 32 x 4 x 36 x 1
x. 3 log x 4 log x 2 5 x 2
4x x 2
xi. 8 4 x
2
5