evaluate the following: log9 27

- anonymous

evaluate the following: log9 27

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- anonymous

do you know how to convert bases?

- anonymous

no ;(

- anonymous

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

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- anonymous

here, 10 is called the base.

- anonymous

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

- anonymous

but im doing log 9?

- anonymous

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

- anonymous

would log9 be converted to 3?

- anonymous

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

- anonymous

3?

- anonymous

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

- anonymous

now, what is log3 27?

- anonymous

so i was rite?

- anonymous

no.

- anonymous

ugh.

- anonymous

answer my question. what is log3 27?

- anonymous

explain it in plain english for now.

- anonymous

9?

- anonymous

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.

- anonymous

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

- anonymous

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

- anonymous

it is not hard at all.

- anonymous

what is 4 to the power 2?

- anonymous

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

- anonymous

2?

- anonymous

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.

- anonymous

oh yah okay thats simple

- anonymous

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

- anonymous

4^2

- anonymous

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

- anonymous

16

- anonymous

just give me the number. Use your calculator.

- anonymous

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

- anonymous

4^3

- anonymous

i know my powers mister

- anonymous

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

- anonymous

48

- anonymous

it is 64.

- anonymous

i multiplyed it wrong. sorry

- anonymous

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?

- anonymous

find the number in the middle?

- anonymous

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

- anonymous

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

- anonymous

ya 4 times 8

- anonymous

no

- anonymous

what is the value of log base 5 512

- anonymous

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?

- anonymous

without calculator

- anonymous

you cant? it would be in a decimal rite?

- anonymous

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

- anonymous

thankyou!

- anonymous

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

- anonymous

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?

- anonymous

idk sathiprakash

- anonymous

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

- anonymous

ok.

- anonymous

right

- anonymous

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?

- anonymous

do you have a calculator, margaret?

- anonymous

right so it would turn into a decimal

- anonymous

i can get it

- anonymous

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

- anonymous

just copy paste that in google.

- anonymous

=32

- anonymous

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

- anonymous

even my problem log9 27

- anonymous

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

- anonymous

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

- anonymous

so it will convert to 3

- anonymous

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

- anonymous

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

- anonymous

what is 3^3?

- anonymous

9?

- anonymous

no, try again.

- anonymous

wait no its 3

- anonymous

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

- anonymous

yes

- anonymous

so what is 3 times 3 times 3?

- anonymous

27

- anonymous

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

- anonymous

3

- anonymous

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

- anonymous

27

- anonymous

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.

- anonymous

so, try again. what does log3 9?

- anonymous

2?

- anonymous

very good!

- anonymous

so what is log3 27 / log3 9?

- anonymous

3/2

- anonymous

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

- anonymous

go on, type it in google.

- anonymous

it is

- anonymous

thankyou very much

- anonymous

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.

- anonymous

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

- anonymous

yes sir i do now

- anonymous

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.

- anonymous

alright i will

- anonymous

okay. good. bye now.

- anonymous

go ahead, take a medal then.

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