1. Logarithmic Functions Mrs. White Algebra II

2. What are logarithms? The inverse of the exponential function!

3. Graph: http://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htm

4. Definitions of Logarithms The logarithmic function is the function, where b is any number such that is equivalent to The function is read "log base b of x".

5. 10 3 = 1000log 10 1000 = 3 2 4 = 16log 2 16 = 4 10 4 = 10,000log 10 10000 = 4 3 2 = 9log 3 9 = 2 4 2 = 16log 4 16 = 2 10 -2 = 0.01log 10 0.01 = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / 2 36 1/2 = 6 log 12 1= 012 0 = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

6. 10 3 = 1000log 10 1000 = 3 2 4 = 16log 2 16 = 4 10 4 = 10,000log 10 10000 = 4 3 2 = 9log 3 9 = 2 4 2 = 16log 4 16 = 2 10 -2 = 0.01log 10 0.01 = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / 2 36 1/2 = 6 log 12 1= 012 0 = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

7. 10 3 = 1000log 10 1000 = 3 2 4 = 16log 2 16 = 4 10 4 = 10,000log 10 10000 = 4 3 2 = 9log 3 9 = 2 4 2 = 16log 4 16 = 2 10 -2 = 0.01log 10 0.01 = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / 2 36 1/2 = 6 log 12 1= 012 0 = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

8. 10 3 = 1000log 10 1000 = 3 2 4 = 16log 2 16 = 4 10 4 = 10,000log 10 10000 = 4 3 2 = 9log 3 9 = 2 4 2 = 16log 4 16 = 2 10 -2 = 0.01log 10 0.01 = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / 2 36 1/2 = 6 log 12 1= 012 0 = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

9. 10 3 = 1000log 10 1000 = 3 2 4 = 16log 2 16 = 4 10 4 = 10,000log 10 10000 = 4 3 2 = 9log 3 9 = 2 4 2 = 16log 4 16 = 2 10 -2 = 0.01log 10 0.01 = -2 log 4 64 = 34 3 = 64 log 3 27 = 33 3 = 27 log 36 6 = 1 / 2 36 1/2 = 6 log 12 1= 012 0 = 1 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q log x y = zx z = y log a 5 = ba b = 5 log p q = rp r = q c = log a bb = a c pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt

10. Change of Base Formula

11. The Formula

12. Examples

13. Homework 9.3 Worksheet #3 Change of Base Formula