anonymous
  • anonymous
This is my first time doing "log". So there is this question saying "evaluate. log5^5." What to do in here?? thanks!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
log a^x = x times log a so log 5^5 = 5 x log 5 = 5 log5
anonymous
  • anonymous
Greetings Keita, If y=a^x then log y (base a) = x
anonymous
  • anonymous
So the answer is 5 log5? hm... my teacher wrote the answer on the whiteboard and she wrote it as 1. btw, 5 after log is down below. and then ^5.

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anonymous
  • anonymous
you mean like this? \[\log_{5}5 \]
anonymous
  • anonymous
yes. like that..
anonymous
  • anonymous
yes write, the question was log 5 (base 5) [cannot write it as the eqn editor is not working] so if you put it in the thing i wrote above it will come out to be 1
anonymous
  • anonymous
oh. then the answer is 1.
anonymous
  • anonymous
Log of anything to to the base of itself it 1
anonymous
  • anonymous
do one thing. copy and paste 4^2.5 in google and tell me what the answer is.
anonymous
  • anonymous
ok I'll google it. @ amogh, so how to solve it? do you know?
anonymous
  • anonymous
I guess dhatraditya is proceeding correctly.
anonymous
  • anonymous
@ dhatraditya it's equal to 32.
anonymous
  • anonymous
@amogh oh.. ok.
anonymous
  • anonymous
@Keita: do you know what x^(1/2) means?
anonymous
  • anonymous
okay good. the answer is 32. but what does 4^2.5 mean? can you say it out in english?
anonymous
  • anonymous
4 to the power of 2.5? x to the power of 1/2?
anonymous
  • anonymous
okay good. does that make sense to you? you know that 4 squared is 16. you know that 4 cubed is 64 in other words, 4 squared is 4*4 4 cubed is 4*4*4 what is 4^2.5?
anonymous
  • anonymous
hm... no idea ...
anonymous
  • anonymous
4^2 = 4^1 * 4^1 correct?
anonymous
  • anonymous
yup..
anonymous
  • anonymous
so 4^2 = 4^1*4^1 = 4^(1+1) similarly 4^2.5 = 4^1 * 4^1 * 4^0.5
anonymous
  • anonymous
but what do we mean by 4^0.5? we mean 4^(1/2) = square root of 4 = 2 so 4^2.5 = 4*4*2 = 32
anonymous
  • anonymous
the lesson to be learned here is that any positive number can be expressed as a power of any other positive number.
anonymous
  • anonymous
go ahead and try 3^2.5 in google
anonymous
  • anonymous
it's 15.5884573.
anonymous
  • anonymous
ah, now try 3*3*sqrt 3
anonymous
  • anonymous
um.. it's same answer. 15.5884573.
anonymous
  • anonymous
great! so do you see a pattern here? we were able to express the number 15.5884573 as a power of 3.
anonymous
  • anonymous
it so happens that any number can be expressed as a power of 3. go ahead and try 3^2.234234 and 3^ (any number you want)
anonymous
  • anonymous
logarithm is the inverse of this process. it means that log 32 = 2.5 in base 4. this means that 4^2.5 = 32 and log 15.5884573 = 2.5 in base 3. this means that 3^2.5 = 15.5884573
anonymous
  • anonymous
32 can also be expressed in base 10, or base 2. try lg 32 in google. that means log to the base 2 of 32 also try log 32. that means log to the base 10 of 32.
anonymous
  • anonymous
log 32=1.50514998 in google. which is near to 2. so, log 5^5? how to do this?
anonymous
  • anonymous
so in your problem \[\log_{5}5 \] it means log 5 to the base 5.
anonymous
  • anonymous
log5^5 has a different meaning. it means log 5 raised to the power 5.
anonymous
  • anonymous
anyway, try 10^1.50514998 in google
anonymous
  • anonymous
it's 32.0000001. yeah, I wrote that way cause I can't write the real one in my computer. so I put it as 5^5...
anonymous
  • anonymous
okay. do you see a relationship here? log 32(to the base 10) = 1.505 and 10^1.505 = 32.
anonymous
  • anonymous
so lets say log 5 to the base 5 = x. what must this mean?
anonymous
  • anonymous
yup, I understand that now..
anonymous
  • anonymous
hm... it means 5 is expressed in base 5. So that means log to the base 5 of 5??
amistre64
  • amistre64
log5(5) = y :means: 5^y = 5 What does 'y' have to equal for this to be true?
anonymous
  • anonymous
hmm. 1. bcoz 5^1 is 5, isn't it?

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