Logarithms An Introduction

Logarithms An Introduction - Transcript

Logarithms An Introduction

Check for Understanding 3103 3 16 Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems

Check for Understanding 3103 3 17 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
pH

Scale

Telecommunication Electronics Optics Astronomy Computer Science Acoustics

Richter Scale Decibels Radioactive Decay Population Growth Interest Rates

And Many More

My calculator has a log button why can t I just use that
The button on your calculator only works for certain types of logarithms these are called common logarithms

Try These On Your Calculator
log245 1 6532 5 4919 log10100

X

2



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 b x b 0 b 1 x 0
y

Write each equation in exponential form

1 log6 36 2 6 36
2

2 log125 5 1

125 5

5

1 5

Write each equation in logarithmic form

3 23 8

log2 8 3

4 7 1 49
1 log 49 7

2

2

Evaluate each expression
5 log4 64 x 4 64 4 4 x 3
x
3

6 log5 625 x 5 625 5 54 x 4
x x

x

Evaluate each expression
7 log2 128 9 log8 4

1 8 log3 81

10 log11 1

Evaluate each expression
7 log2 128 7 9 log8 4 10 log11 1 0

1 8 log3 81
4

Solve each equation
11 log4 x 3 4 x 64 x
3

12 log4 x 3 2 4 x x 8
3 2

Evaluate each expression
13 log6 2y 8 2

15 log7 5x 7 log7 3x 11

14 logb 16 4

16 log3 2x 8 log3 6x 24

Evaluate each expression
13 log6 2y 8 2

15 log7 5x 7 log7 3x 11 2 16 log3 2x 8 log3 6x 24

14
14 logb 16 4 2