Question

This is my first time doing "log". So there is this question saying "evaluate. log5^5." What to do in here?? thanks!!

Answer 1

log a^x = x times log a
so log 5^5 = 5 x log 5 = 5 log5

Answer 2

Greetings Keita,
If y=a^x
then log y (base a) = x

Answer 3

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.

Answer 4

you mean like this?
\[\log_{5}5 \]

Answer 5

yes. like that..

Answer 6

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

Answer 7

oh. then the answer is 1.

Answer 8

Log of anything to to the base of itself it 1

Answer 9

do one thing. copy and paste
4^2.5 in google and tell me what the answer is.

Answer 10

ok I'll google it. @ amogh, so how to solve it? do you know?

Answer 11

I guess dhatraditya is proceeding correctly.

Answer 12

@ dhatraditya it's equal to 32.

Answer 13

@amogh oh.. ok.

Answer 14

@Keita: do you know what x^(1/2) means?

Answer 15

okay good. the answer is 32. but what does 4^2.5 mean? can you say it out in english?

Answer 16

4 to the power of 2.5? x to the power of 1/2?

Answer 17

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?

Answer 18

hm... no idea ...

Answer 19

4^2 = 4^1 * 4^1 correct?

Answer 20

yup..

Answer 21

so 4^2 = 4^1*4^1 = 4^(1+1)
similarly 4^2.5 = 4^1 * 4^1 * 4^0.5

Answer 22

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

Answer 23

the lesson to be learned here is that any positive number can be expressed as a power of any other positive number.

Answer 24

go ahead and try 3^2.5 in google

Answer 25

it's 15.5884573.

Answer 26

ah, now try 3*3*sqrt 3

Answer 27

um.. it's same answer. 15.5884573.

Answer 28

great! so do you see a pattern here? we were able to express the number 15.5884573 as a power of 3.

Answer 29

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)

Answer 30

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

Answer 31

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.

Answer 32

log 32=1.50514998 in google. which is near to 2. so, log 5^5? how to do this?

Answer 33

so in your problem
\[\log_{5}5 \]
it means log 5 to the base 5.

Answer 34

log5^5 has a different meaning. it means log 5 raised to the power 5.

Answer 35

anyway, try 10^1.50514998 in google

Answer 36

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...

Answer 37

okay. do you see a relationship here?
log 32(to the base 10) = 1.505
and 10^1.505 = 32.

Answer 38

so lets say log 5 to the base 5 = x.
what must this mean?

Answer 39

yup, I understand that now..

Answer 40

hm... it means 5 is expressed in base 5. So that means log to the base 5 of 5??

Answer 41

log5(5) = y :means: 5^y = 5

What does 'y' have to equal for this to be true?

Answer 42

hmm. 1. bcoz 5^1 is 5, isn't it?