evaluate the following: log9 27

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evaluate the following: log9 27

Mathematics
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do you know how to convert bases?
no ;(
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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here, 10 is called the base.
so log10 13 = 1.114 This means that logarithm of 13 to the base 10 is 1.114
but im doing log 9?
13 can also be expressed as 2 to the power 3.7004. which means log 2 13 = 3.7004
would log9 be converted to 3?
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
3?
following the logic of that link, we can say that log9 27 = log3 27/ log3 9
now, what is log3 27?
so i was rite?
no.
ugh.
answer my question. what is log3 27?
explain it in plain english for now.
9?
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.
its harrd. okay, we would put log3/log3 27?
do you understand the meaning of logs? I posted it earlier. READ through it.
it is not hard at all.
what is 4 to the power 2?
ya its hard im not a smart cookie like you. i dont no where you got the decimals from your example???!!
2?
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.
oh yah okay thats simple
so give me the answer. what is 4 raised to the power 2?
4^2
right, what is the value of 4^2? 4^2 = 4*4 right? what is 4*4?
16
just give me the number. Use your calculator.
right. okay great!. what is 4 raised to the power 3?
4^3
i know my powers mister
thats good to know. I am asking the value of 4^3.
48
it is 64.
i multiplyed it wrong. sorry
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?
find the number in the middle?
I want you to express the number 32 as a power of 4. Can you do it?
what if I wanted 17 as a power of 4, or 18?
ya 4 times 8
no
what is the value of log base 5 512
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?
without calculator
you cant? it would be in a decimal rite?
exactly! you are on the right track margaret! very well done!
thankyou!
conditions are given like log 2 = 0.3010 and log 3= 0.4771......so whats the value of log base 5 512?
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?
idk sathiprakash
sathiprakash if you have a separate problem please post it elsewhere. you are confusing the learning process here.
ok.
right
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?
do you have a calculator, margaret?
right so it would turn into a decimal
i can get it
okay doesnt matter. use google. it has a calculator built in. paste this exactly. 4^2.5
just copy paste that in google.
=32
great! so you see? any number can be expressed as a power of 4!
even my problem log9 27
So we call 4 the base. similarly in your problem, the base is 9.
so we need to find what power we need to raise 9 to get 27.
so it will convert to 3
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
so what power do you need to raise 3 to get 27? do you know?
what is 3^3?
9?
no, try again.
wait no its 3
no. 3^3 = 3*3*3 correct?
yes
so what is 3 times 3 times 3?
27
great! so what is log3 27? In other words, what power do you need to raise 3 in order to get 27?
3
very good! so then by the same logic, what is log3 9?
27
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.
so, try again. what does log3 9?
2?
very good!
so what is log3 27 / log3 9?
3/2
good. so your answer is 1.5. now go ahead and check your answer. see if 9^1.5 is 27
go on, type it in google.
it is
thankyou very much
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.
you are welcome. I hope you understood the meaning behind logs and powers and bases.
yes sir i do now
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.
alright i will
okay. good. bye now.
go ahead, take a medal then.

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