Logarithms An Introduction Check for Understanding 3103 3

Logarithms – An Introduction Check for Understanding – 3103. 3. 16 Check for Understanding – 3103. 3. 17 Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems. Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems.

What are logarithms? log·a·rithm : noun the exponent that indicates the power to which a base number is raised to produce a given number Merriam-Webster Online (June 2, 2009)

What are logarithms used for? • p. H Scale • Telecommunication • Richter Scale • Electronics • Decibels • Optics • Radioactive Decay • Astronomy • Population Growth • Computer Science • Interest Rates • Acoustics … And Many More!

My calculator has a log button… why can’t I just use that? The button on your calculator works only for certain types of logarithms; these are called common logarithms.

Try These On Your Calculator log 245 log 10100 1. 6532 X 5. 4919 P 2 P

What’s the difference? The log button on the calculator is used to evaluate common logarithms, which have a base of 10. If a base is not written on a logarithm, the base is understood to be 10. log 100 is the same as log 10100

The logarithmic function is an inverse of the exponential function.

Logarithm with base b The basic mathematical definition of logarithms with base b is… y logb x = y if b = x b > 0, b ≠ 1, x > 0

Write each equation in exponential form. 1. log 6 36 = 2 2 6 = 36 2. log 125 5 = 1 5 125 = 5

Write each equation in logarithmic form. 3. 23 = 8 log 2 8 = 3 -2 4. 7 = 1 49 log 7 = – 2

Evaluate each expression 5. log 4 64 = x x 4 = 64 x 4 =4 x=3 3 6. log 5 625 = x x 5 = 625 x 5 =5 x=4 4

Evaluate each expression 7. log 2 128 8. log 3 9. log 8 4 10. log 11 1

Evaluate each expression 7. log 2 128 7 8. log 3 – 4 9. log 8 4 ⅔ 10. log 11 1 0

Solve each equation 11. log 4 x = 3 3 4 =x 64 = x 12. log 4 x = 3 2 4 =x x=8

Evaluate each expression 13. log 6 (2 y + 8) = 2 15. log 7 (5 x + 7) = log 7 (3 x + 11) 14. logb 16 = 4 16. log 3 (2 x – 8) = log 3 (6 x + 24)

Evaluate each expression 13. log 6 (2 y + 8) = 2 14 14. logb 16 = 4 2 15. log 7 (5 x + 7) = log 7 (3 x + 11) 2 16. log 3 (2 x – 8) = log 3 (6 x + 24)