Question

Write in exponential form. (Will write in equation editor)

Answer 1

\[5^{\log5}^{25}\]

Answer 2

wait..that came out funny..

Answer 3

\[5^{\log5}\]

Answer 4

There is suppoesd to be a 25 next to log 5

Answer 5

\[ 5^{log{5}^{25}}\] ?

Answer 6

\[\huge 5^{(\log5)^{25}}\]?

Answer 7

is 5 the base of the logarithm ?

Answer 8

Turing Test wrote it correctly.

Answer 9

I know how to do it, just am confused about the 5 in the front. what do i do with it?

Answer 10

the the exponent of the log can come out the front
\[5^{log(5)^{25}}=5^{25(log(5)}\]

Answer 11

Thats it? I am still confused.

Answer 12

\[5^{25\log5}\neq5^{25}\times5^{\log5}\]

Answer 13

I have made an error turing test?

Answer 14

\[\log_5(25)=2\]you are tired

Answer 15

I am reading this off of my math book. 5 is the big dog, while \[\log _{5}25\] is above it.

Answer 16

oh yeah i see how wrong that is now

Answer 17

well now that we've got it sorted out the problem is trivial
goodman please try to post more clearly, that is not what you originally wrote

Answer 18

errors ervery where,
perhaps i should just watch and learn

Answer 19

How did you get that? @TuringTest

Answer 20

\[\huge 5^{\log_5(25)}=5^2=25\]because\[\huge 5^2=25\]

Answer 21

I appologize, srry, i did read it wrong. srry srry.

Answer 22

I am new to log, so yea, srry.

Answer 23

but in general\[\huge a^{\log_a(x)}=x\]so we could have skipped that analaysis

Answer 24

Oh yea, because it always is equal to the front number. Yea, okay, got it :D Thanx, srry for the mix up :/

Answer 25

it's ok, let me know if you have more questions

Answer 26

You are familiar with log? Because dont understand em at all :P

Answer 27

yes, they can be a bit tricky at first
think about small numbers
first the definition as I like to give it:\[\huge\log_ax=b\text{ if }a^b=x\]in other words\[\large \log_ax\]asks
"what power do we raise a to in order to get x?"
for example...

Answer 28

\[\large\log_2(4)\]asks
"2 raised to what power equals 4?"
so what is the answer?

Answer 29

2 rite?

Answer 30

right
because 2^2=4
so what about\[\log_2(16)\]?

Answer 31

4

Answer 32

right
so now you should see why\[\log_5(25)=2\]yes?

Answer 33

YES!! wow!! It is 5 because 5^5 is equal to 25

Answer 34

\[5^2\]

Answer 35

Whoops..srry, so the exponent is the answer?

Answer 36

yeah\[\log_2(16)=4\]as you said, because\[2^4=16\]

Answer 37

Is that always the case?

Answer 38

so\[\log_5(25)=2\]because\[5^2=25\]

Answer 39

in general we have\[\huge\log_a(x)=y\iff a^y=x\]so yes, that means always
you could say that the question is on the left:
"a to what power equals x?"
the answer is on the right
"a to the y equals x"

Answer 40

so do some more
what is\[\log_4(16)\]?

Answer 41

2

Answer 42

right\[\log_{10}(10000)\] ?

Answer 43

umm..lol, 1000

Answer 44

I think i got it wrong

Answer 45

the question is
"10 to what power equals 10000"
you are asserting that\[\large10^{1000}=10000\]which I dont think you believe
what is\[10^2\] ?

Answer 46

Wait..no, its 100

Answer 47

\[10^{100}\neq10000\]

Answer 48

So what is it?

Answer 49

I dont have a calculator rite now :P

Answer 50

\[10^2=10\cdot10=100\]\[10^3=10\cdot10\cdot10=1000\]the exponent on the ten is the number of zeros after the one

so 10 to what power equals 10000 ?

Answer 51

\[10^{4}?\]

Answer 52

exactly
so\[\log_{10}(10000)=4\]because\[10^4=10000\]

Answer 53

That makes its it so simple

Answer 54

yeah that's a handy rule, and is used in science to describe very large and small numbers
last one:
how about\[\log_3(81)\]

Answer 55

4

Answer 56

right :D
do you know the basic log rules\[\log(ab)=\log a+\log b\]\[\log(\frac ab)=\log a-\log b\]\[\log(a^b)=b\log a\]?

Answer 57

No, we havent been taught those. We started log in class today.

Answer 58

when you start using that things will be easier
\[\large \log(ab)=\log a+\log b\text{ because }x^a\cdot x^b=x^{a+b}\]for example
it takes a bit to get used to those ideas though

Answer 59

Yea, just by reading it, I understand the first function.

Answer 60

I also understand the second one, the third one looks funny.

Answer 61

the third one can be illustrated by the problems we just did
first I will ask you what is\[\log_22\]?

Answer 62

1

Answer 63

lol, i find myself saying "2 raised to what power is 2" thats a neat trick

Answer 64

I'm glad, it helps me!
and in general\[\log_aa=1\]now look at\[\log_2(16)\]if we factor 16 we get\[\log_2(2^4)\]now apply the third rule\[4\log_2(2)=4(1)=4\]so we get the answer we already knew
it also shows that\[\log_aa^x=x\]which is nice to know that's how I did your earlier problem)
so by factoring and using these rules we can break down lots of numbers with logs

Answer 65

now here's the last grand example\[\log_2(24)=\log_2(2^3\cdot3)\]using the first rule\[\log_2(2^3)+\log_23\]and now the third\[3\log_2(2)+\log_23=3+\log_23\]and that's as far as it goes

Answer 66

Wow, i never knew log could be so simple :D

Answer 67

I'm glad you feel that way :D

Answer 68

Thanx a ton :D I am now cleared up on log, thank you thank you!!!

Answer 69

happy to help!