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3. What is log? Here we use shortcuts to exponentials for speedy calculations. logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce that number. For example, the logarithm of 1000 to base 10 is 3 it can be written as : log 10 1000 = 3 usually we use the base of 10, so we can write : log 1000 = 3

4. What is log 10 100000? = 5 answer

5. What is natural log ? Here the base is e, which is 2.71828 (not 10, which we had discussed earlier).

6. What is log 2 8? = 3 (here base is 2, and we know that 2^3 = 8)

7. What is log 1982 1? Answer = 0 We know that in any base b, the logarithm of 1 is 0.

8. What is log b b^x = ? Answer = x it is a rule that : log b b^x = x

9. What is : 5 = log 2 n ( what is n?) 32 (answer ) 2^5 = 32

10. What is log 10 .001 = -3

11. Find log of 1728 to the base 2*sqrt(3) ? Let us take factors of 1728 : 2*2*2*2*2*2*3*3*3 thus we know that 2*sqrt(3) ^ 6 = 1728 so answer is 6.

12. Change the base of log 200 to 2? = log 2 200 / log 2 10

13. Given: log 2 = .3010 log 3 = .4771 log 5 = .6990, what is log 6? We know that log 6 = log 2 * 3 we know that log 2*3 = .3010+.4771 =.7781

14. Given: log 2 = .3010, log 3 = .4771 Evaluate log 18. Log 2 * log 3*log 3 =.3010+.4771+.4771 =1.2552

15. Given: log 6 = .7781 Use the laws of logarithms to evaluate log 600 =log 6 * 100 = .7781 + 2 = 2.7781 answer