Exponential and Logarithmic Forms of Equations
(2nd) Definition of a Logarithm:
If b and N are positive numbers (b  1), logbN = k if and only if bk = N
logb N = k is called the logarithmic form. bk = N is the exponential form.
***LEARN HOW TO SWITCH FORMS NOW!!!
Write each equation in exponential form.
1. log28 = 3
1
2. log2 = -2
4
Notice: A logarithm is equal to the power you would have to raise the base to, to get the number you
are taking the “log” of… How is this similar to radicals and powers? How is it not?
3. log21 = 0
5. log162 =
1
4
4. log381 = 4
6. log82 =
Write each equation in log form.
7. 24 = 16
1
5
8. 2-1 =
1
2
9. 32 = 2
10. 82= 64
11. 50 = 1
12. 61 = 6
1
3
N 10-4
Evaluate the following logarithms without using a calculator.
13. log525 = _____
14. log464 = _____
15. log4(-16) = _____
16. log10103 = ______
17. log3 1 = _____
3
18. log93 = _____
19. log16 1 = _____
2
N 10-4