Question

Rewrite 1000^log_base10(x) as an expression of x without logs.

Answer 1

firstly, do you know this rule:\[\log_ab=c\implies b=a^c\]

Answer 2

?

Answer 3

Sorry to go dark. I had to go to work. Forgot to log out. Yes, I do know that rule. I get that logs are the inverse of exponentials, but somehow the notation always seems to confuse me, and I'm not quite sure what to do with the log in the exponent.

Answer 4

hint : \(10^ {log_{10} x} = x \)

Answer 5

So, when the x comes down from the log, why isn't it 10^x?

Answer 6

u familiar wid inverse functinons ?

Answer 7

if u let,
f(x) = log x
g(x) = 10^x

then, g is the inverse of f

so,

g(f(x)) = x

Answer 8

Yes. It's just something about the notation that makes it hard for me to get a handle on. Log is the inverse of exponential.

Answer 9

u take log of 'something', then exponent of the result, u get ur 'something' back

Answer 10

For some reason this isn't clicking, though.

Answer 11

see it in two steps,

first step u take log
next step u take exponent

Answer 12

x^10?

Answer 13

almost... but not quite correct


\(\huge 1000^{\log_{10}(x)} \)

Answer 14

\(\huge (10^3)^{\log_{10}(x)} \)

Answer 15

see if u can simplify now :)

Answer 16

The x comes down, and the base is the exponent, no?

Answer 17

And then, I'm still not sure what to do with the thousand.

Answer 18

why would x come down ?

Answer 19

Well, if x is the log, that means it it is the power of the base, right?

Answer 20

I feel like I'm making this more complicated than it needs to be.

Answer 21

...which is a recurring theme in my mathematical endeavors.

Answer 22

log10(100)=2

Answer 23

noo ur logic is correct,

but we're taking log base 10 for x, but in the bottom we have 1000, so x wont come down !

Answer 24

for x to come down, we need to have 10 in the bottom, not 1000

Answer 25

Not that bottom. I'm not being precise enough, I guess.

Answer 26

\(10^{\log_{10}SOMETHING } = SOMETHING\)

Answer 27

I should have said...out? 10 to the something is x?

Answer 28

\(\huge (10^3)^{\log_{10}(x)} \)

how it would become, based on ur thinking ?

Answer 29

ok.. hey im getting late , need to go... hope u would get these cleared up by someone else... good luck cya

Answer 30

Um, thanks.

Answer 31

np :)

Answer 32

um can any of yall help me on my ? please

Answer 33

I can't even seem to get mine figured out. :-/

Answer 34

mine is about my ipod touch 2g

Answer 35

Then I think you're doing it wrong. This is a thread about Calculus.

Answer 36

no its techly the geek section on open study lmfao

Answer 37

http://www.cliffsnotes.com/study_guide/Logarithmic-Functions.topicArticleId-10792,articleId-10791.html this will help with your issue then lol now please help with mine

Answer 38

@double.emms - going back to my original statement above:\[\log_ab=c\implies b=a^c\]now, if you substitute the expression for c (i.e. \(c=\log_ab\)) into:\[b=a^c\]you end up with:\[b=a^c=a^{\log_ab}\]Hence:\[a^{\log_ab}=b\tag{1}\]Next I assume you also know this law of indicies:\[(x^a)^b=x^{ab}=(x^b)^a\tag{2}\]
Now take a close look at your question:\[1000^{log_{10}x}=(10^3)^{log_{10}x}\]Make use of the relations in (1) and (2) and see if you can solve from here.