1. Express 53 = 125 in logarithm form.
2. Express log101 = 0 in exponential form.
3. Find the log of 32 to the base 4.
4. Find x if log5(x-7)=1.
5. If logam=n, express an-1 in terms of a and m.
6. Solve for x if log(x-1)+log(x+1)=log21
7. Express log(75/16)-2log(5/9)+log(32/243) in terms of log 2 and log 3.
8. Express 2logx+3logy=log a in logarithm free form.
9. Prove that: 2log(15/18)-log(25/162)+log(4/9)=log2
10. Express log10(2) + 1 in the form of log10x.
11. Find the value of x, if log10(x-10)=1.
12. Find the value of x, if log(x+5)+log(x-5)=4log2+2log3
13. Solve for x, if (log 225/log15) = log x
14. Convert 0.00000046 into scientific notation.
15. Convert 301000000 in scientific notation.
16. Convert 1.36 × 107 from scientific notation to standard notation.
17. Using logarithmic table find the value of the following.
(i)
log329.5
(ii) (iv) log0.001364
18. Using antilogarithmic table find the value of the following.
(i) antilog3.072 (ii) antilog0.2732
19. The mantissa of log23750 is 0.3756. Find the value of
the following.
(i) log23750
(ii) log0.00002375
20. Find the conjugate of the following numbers.
(i)
4
5
−5 ,4
(ii) 3+4i
21. Find x and y in this complex number if :
4x+3yi = 16 + 9y
22. If Z1 = 6+9i and Z2 = -1 + 2i, find the following:
(i)
Z1 + Z2 (ii) Z1 - Z2 (iii) Z1 x Z2 (iv) Z1 ÷ Z2
23. Mark the following expressions (P) if polynomial or (NP) if not polynomial
(i)
5x4 - 7x
(ii)
3
5𝑦 2
(iii) −6𝑚5 𝑛 + 2 𝑚
(iv) −3𝑝2 𝑞 − 4𝑝 + 2𝑝7 𝑞𝑟 + 𝑞 −4 +5
(v) −𝑎2 𝑏
4
(vi) 5𝑥 2 + 𝑥 2+𝑥 + 𝑥 5
1
(vii) 6𝑔4 ℎ5
24. Mark the following expressions (R) if rational or (Ir) if irrational.
𝑥+9
(i) 𝑥 −3 −7
(i)
5𝑥 2 −8
2𝑥−1
(ii)
𝑥 3 +5𝑥 2 −12𝑥+1
𝑥 4 −10
(iii)
3
8
25. Perform indicated operation and reduce the answer to lowest form.
(i)
3
𝑥+1
𝑥+4
𝑥 2 +11𝑥+10
𝑥 2 −49
𝑥 2 −𝑥−42
(ii) 2𝑥 2−3𝑥−5 ÷ 𝑥 2+7𝑥+6
26. Expand and simplify the following expressions
(i) 8𝑥 3 − 343
(ii) 8𝑥 3 − 18𝑥 2 𝑦 + 18𝑥𝑦 2 − 27𝑦 3
27. Rationalize:
4
1+2 3
28. Simplify:
3
40𝑥 4 𝑦 5
29. 15973 = ?
30. 4680 = ?