1. 1 Logarithms Definition If y = a x then x = log a y For log 10 x use the log button. For log e x use the ln button.

2. 2 Logarithms Examples Log 10 5.3 =0.724275869 ≈0.7 Log 10 53 = 1.724275869 ≈1.7 Log 10 530 = 2.724275869 ≈2.7 Log e 5.3 =1.667706821 ≈1.7 Log e 53 = 3.970291914 ≈4.0 Log e 530 = 6.272877007 ≈6.3

3. 3 Logarithms Example 1 Log 3 27 = x If y = a x then x = log a y 27 = 3 x 3 3 = 3 x x = 3 y = 27 a = 3 x = x

4. 4 Logarithms Example 2 Log 3 81 = x If y = a x then x = log a y 81 = 3 x 3 4 = 3 x x = 4 y = 81 a = 3 x = x

5. 5 Logarithms Example 3 Log 2 64 = x If y = a x then x = log a y 64 = 2 x 2 6 = 2 x x = 6 y = 64 a = 2 x = x

6. 6 Logarithms Example 4 Log 2 1 / 4 = x If y = a x then x = log a y 1/4 =1/4 = 2 x 2 -2 = 2 x x = -2 y = 1 / 4 a = 2 x = x