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do you know how to convert bases?
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
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
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?
answer my question. what is log3 27?
explain it in plain english for now.
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???!!
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?
right, what is the value of 4^2? 4^2 = 4*4 right? what is 4*4?
just give me the number. Use your calculator.
right. okay great!. what is 4 raised to the power 3?
i know my powers mister
thats good to know. I am asking the value of 4^3.
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
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?
you cant? it would be in a decimal rite?
exactly! you are on the right track margaret! very well done!
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?
sathiprakash if you have a separate problem please post it elsewhere. you are confusing the learning process here.
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.
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?
no, try again.
wait no its 3
no. 3^3 = 3*3*3 correct?
so what is 3 times 3 times 3?
great! so what is log3 27? In other words, what power do you need to raise 3 in order to get 27?
very good! so then by the same logic, what is log3 9?
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?
so what is log3 27 / log3 9?
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.
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.