1. Logarithmic Functions Mrs. King Pre-Calculus

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

3. Graph: Picture from: http://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htm Regardless of the base, the exponential graph goes through the point (0,1). Therefore, regardless of the base, the logarithmic graph goes through the point (1,0).

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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

10. 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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

11. 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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

12. 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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

13. 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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

14. 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 p = q 2 log q p = 2 x y = 2log x 2 = y p q = rlog p r = q pifactory.net/catalog/files/teacher_resources/.../logarithms_01.ppt Rewrite using logarithms

15. 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 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 Rewrite using exponential notation

16. 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 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 Rewrite using exponential notation

17. 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 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 Rewrite using exponential notation

18. 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 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 Rewrite using exponential notation

19. 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 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 Rewrite using exponential notation

20. 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 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 Rewrite using exponential notation

21. 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 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 Rewrite using exponential notation

22. 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 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 Rewrite using exponential notation

23. 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 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 Rewrite using exponential notation

24. The Change of Base Formula

25. Examples…watch your parenthesis!