Logarithms – An Introduction Check for Understanding – 3103.3.16 Prove basic properties of...
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Logarithms – An Introduction Check for Understanding – 3103.3.16 Prove basic properties of logarithms using properties of exponents and Check for Understanding – 3103.3.17 Know that the logarithm and exponential functions are inverses and use this informat to solve real-world problems
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Transcript of Logarithms – An Introduction Check for Understanding – 3103.3.16 Prove basic properties of...
Logarithms – An Introduction
Check for Understanding – 3103.3.16
Prove basic properties of logarithms using propertiesof exponents and applythose properties to solveproblems.
Check for Understanding– 3103.3.17
Know that the logarithm andexponential functions are
inverses and use this informationto 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?
• pH Scale
• Richter Scale
• Decibels
• Radioactive Decay
• Population Growth
• Interest Rates
• Telecommunication
• Electronics
• Optics
• Astronomy
• Computer Science
• Acoustics
… And Many More!
My calculator has a log button…
why can’t I just use that?
The button on your calculator only worksfor certain types of logarithms; these are called common logarithms.
Try These On Your Calculator
log245 log
10100
2 X1.6532
5.4919
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 log10100
The logarithmic function is an inverse of the exponential function.
Logarithm with base b
The basic mathematical definition of logarithms with base b is…
logb x = y iff by = x
b > 0, b ≠ 1, x > 0
Write each equation in exponential form.
1. log6 36 = 2
62 = 36
2. log125 5 = 1
5
1
5 = 5125
Write each equation in logarithmic form.
3. 23 = 8
2= 3
4. 7-2 = 1 49
log
= –2
log 8
7
1
49
Evaluate each expression
5. log4 64 = x 6. log5 625 = x
4x = 64 5x = 625
4x= 43
x = 3
5x= 54
x = 4
Evaluate each expression
7. log2 128
8. log3
9. log8 4
10. log11 1
1
81
Evaluate each expression
7. log2 128
7
8. log3
–4
9. log8 4
⅔
10. log11 1
0
1
81
Solve each equation
11. log4 x = 3 12. log4 x = 3 2
43 = x
64 = xx = 8
43
2 = x
Evaluate each expression
13. log6 (2y + 8) = 2
14. logb 16 = 4
15. log7 (5x + 7) = log7 (3x + 11)
16. log3 (2x – 8) = log3 (6x + 24)
Evaluate each expression
13. log6 (2y + 8) = 2
14
14. logb 16 = 4
2
15. log7 (5x + 7) = log7 (3x + 11)
2
16. log3 (2x – 8) = log3 (6x + 24)
