Aim: What is the common logarithms? Do Now: Evaluate the following log10 1 log1010 log10 100 log10 1000 5. HW: p.335 # 8,20,22,28,32,38,42,50,54,56

In log a, the value of a must be greater than 0 Any logarithm with base 10 is called common log We can write log10 a as log a, that is if the base of a logarithm is not indicated, then its base is 10 Use calculator to find the value of common log 1. log 2.53 2. log 0.8 3. log 0 4. log -2 1. .4031 2. -.0969 3. undefined 4. undefined In log a, the value of a must be greater than 0

If log x = 3.7886, find x to the nearest integer If log a = 0.5733, find log 0.001a Use product rule: log 0.001a = log 0.001 + log a = –3 + 0.5733 = –2.4267

If log N = 3.36486, find N to the nearest integer 103.36486 = 2317 Evaluate log2 6 Since the calculator does not have give log base 2 ,we need to rewrite log2 6 with base 10 Use the formula

Express log N in terms of log x, log y and log z

If log 7.11 = b, then log 7110 equals a) 1000b b) 3b c) 3 + b d) 1000 + b log 7110 = log (7.11 • 1000) = log 7.11 + log 1000 = b + 3 The expression is equivalent to

c 1. Find N to the nearest tenth: log N = .6884 N = 4.9 3. If log x = 1.8837, find x to the nearest tenth x = 76.5 4. If log a = c, then log 100a equals a) 110c b) 2c c) 2 + c d) 2 + log c c 5. The expression is equivalent to b