Question

evaluate the following: log9 27

Answer 1

do you know how to convert bases?

Answer 2

no ;(

Answer 3

okay logarithms work the following way: any number can be expressed as another number to some power
For example 13 can be expressed as 10 to the power 1.114

Answer 4

here, 10 is called the base.

Answer 5

so log10 13 = 1.114 This means that logarithm of 13 to the base 10 is 1.114

Answer 6

but im doing log 9?

Answer 7

13 can also be expressed as 2 to the power 3.7004. which means log 2 13 = 3.7004

Answer 8

would log9 be converted to 3?

Answer 9

so log9 27 = ? the ? is the power to which you have to raise 9 in order to get 27.

http://www.sosmath.com/algebra/logs/log4/log43/log43.html

Answer 10

3?

Answer 11

following the logic of that link, we can say that log9 27 = log3 27/ log3 9

Answer 12

now, what is log3 27?

Answer 13

so i was rite?

Answer 14

no.

Answer 15

ugh.

Answer 16

answer my question. what is log3 27?

Answer 17

explain it in plain english for now.

Answer 18

9?

Answer 19

no, read what I posted earlier. Don't simply dab at answers. Understand the logic behind logs and you wont ever have any more problems with it.

Answer 20

its harrd. okay, we would put log3/log3 27?

Answer 21

do you understand the meaning of logs? I posted it earlier. READ through it.

Answer 22

it is not hard at all.

Answer 23

what is 4 to the power 2?

Answer 24

ya its hard im not a smart cookie like you. i dont no where you got the decimals from your example???!!

Answer 25

2?

Answer 26

okay. I am trying to explain it to you. what is 4 squared? what we mean by 4 raised to the power 2 is 4 squared.

Answer 27

oh yah okay thats simple

Answer 28

so give me the answer. what is 4 raised to the power 2?

Answer 29

4^2

Answer 30

right, what is the value of 4^2? 4^2 = 4*4 right? what is 4*4?

Answer 31

16

Answer 32

just give me the number. Use your calculator.

Answer 33

right. okay great!. what is 4 raised to the power 3?

Answer 34

4^3

Answer 35

i know my powers mister

Answer 36

thats good to know. I am asking the value of 4^3.

Answer 37

48

Answer 38

it is 64.

Answer 39

i multiplyed it wrong. sorry

Answer 40

anyway, the point is this. what if you wanted to express a number between 16 and 64 as a power of 4? what happens then?

Answer 41

find the number in the middle?

Answer 42

I want you to express the number 32 as a power of 4. Can you do it?

Answer 43

what if I wanted 17 as a power of 4, or 18?

Answer 44

ya 4 times 8

Answer 45

no

Answer 46

what is the value of log base 5 512

Answer 47

no no. that is 4 times 8, I want you to express 32 as a power of 4. You can express 16 as the 2nd power of 4 and 64 as the 3rd power of 4. what about 17, 18 , 19 and so on?

Answer 48

without calculator

Answer 49

you cant? it would be in a decimal rite?

Answer 50

exactly! you are on the right track margaret! very well done!

Answer 51

thankyou!

Answer 52

conditions are given like log 2 = 0.3010 and log 3= 0.4771......so whats the value of log base 5 512?

Answer 53

okay. so that is where we use logarithms. so 4 should be raised to a power between 2 and 3 in order to get 32 right?

Answer 54

idk sathiprakash

Answer 55

sathiprakash if you have a separate problem please post it elsewhere. you are confusing the learning process here.

Answer 56

ok.

Answer 57

right

Answer 58

okay margaret, now, so we know that 4^2 is 16 and 4^3 is 64. so to express 32 as a power of 4, we know that the answer must lie between 2 and 3. correct?

Answer 59

do you have a calculator, margaret?

Answer 60

right so it would turn into a decimal

Answer 61

i can get it

Answer 62

okay doesnt matter. use google. it has a calculator built in. paste this exactly. 4^2.5

Answer 63

just copy paste that in google.

Answer 64

=32

Answer 65

great! so you see? any number can be expressed as a power of 4!

Answer 66

even my problem log9 27

Answer 67

So we call 4 the base. similarly in your problem, the base is 9.

Answer 68

so we need to find what power we need to raise 9 to get 27.

Answer 69

so it will convert to 3

Answer 70

right, so what we do is, we convert bases, that is a logarithmic property. I pasted that link earlier. so log9 27 = log3 27/log3 9

Answer 71

so what power do you need to raise 3 to get 27? do you know?

Answer 72

what is 3^3?

Answer 73

9?

Answer 74

no, try again.

Answer 75

wait no its 3

Answer 76

no. 3^3 = 3*3*3 correct?

Answer 77

yes

Answer 78

so what is 3 times 3 times 3?

Answer 79

27

Answer 80

great! so what is log3 27? In other words, what power do you need to raise 3 in order to get 27?

Answer 81

3

Answer 82

very good! so then by the same logic, what is log3 9?

Answer 83

27

Answer 84

no, understand what log3 9 means. It means what power do you need to raise 3 to get 9. that is what log3 9 means.

Answer 85

so, try again. what does log3 9?

Answer 86

2?

Answer 87

very good!

Answer 88

so what is log3 27 / log3 9?

Answer 89

3/2

Answer 90

good. so your answer is 1.5. now go ahead and check your answer. see if 9^1.5 is 27

Answer 91

go on, type it in google.

Answer 92

it is

Answer 93

thankyou very much

Answer 94

so log9 27 = 1.5
in english, it means that logarithm to the base 9 of 27 is 1.5
in other words. raise 9 to the power 1.5 to get 27.

Answer 95

you are welcome. I hope you understood the meaning behind logs and powers and bases.

Answer 96

yes sir i do now

Answer 97

good, I want you to do a little exercise. just pick a number. say 7. let 7 be your base.
raise 7 to 1.2, 1.3,1.4, 2.54444 etc and see what numbers you get in google. You will see that any number can be expressed as a power of 7. not just integers, even fractions can be expressed as powers of 7.

Answer 98

alright i will