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CSE 374: Algorithms 1

Worksheet 1

[Full Marks 22]

You must brush up your logarithm and series summation skills. Read Appendix of CORMEN bookfor the essentials.

Note: Worksheet problems are more like practice problems to hone your skills through better understanding the concepts. They are easier than homework problems. Solution to every problem should preferably be typed (or, very legibly written in hand on letter size pages). Plagiarism in any form will be strictly dealt with following departmental policy. You should try to solve by yourself as much as possible. You can take help of study materials and book resources and office hours.

1.   Are the following sequences arithmetic, geometric, or neither? If they are arithmetic, state the value of d. If they are geometric, state r.   [4]

a) 6, 12, 18, 24, ... _________________________________________

b) 2, 14, 98, 686, ... _______________________________________

2.   Write the following in exponential form:                         [2]

log2  (y/ 3) = 4

3.   Write the following in logarithm form :                           [2]

32 = x5

4.   Use the logarithm laws to simplify                                   [4]

a.   log3  9xy2  −log3 27xy

b.   log3  9x4  −log3 (3x)2

5.   Find x if:                                                                                [4]

a.   2logb 5 +1/2 logb 9−logb 3 = logb x

b.   logb (x + 2)−logb 4 = logb 3x

7.   Solve for x:                                                                            [2]

log10 (2x + 1) = 2