anonymous
  • anonymous
If (log_3 X) (log_5 3) = 3, find x
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Which one of these has an x?
anonymous
  • anonymous
The other one is just a multiplicative constant. You can divide it over to the other side.
anonymous
  • anonymous
?? how? the bases are diff-- three and five...how can u just divide?

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anonymous
  • anonymous
Because the log base 5 of 3 is just a number. Like 4/5 or the square root of 15
anonymous
  • anonymous
=( i still don't get it....
anonymous
  • anonymous
Ok here. Lets say that \[C=log_5 3\] Now your equation looks like: \[C(log_3 x) = 3\] Can you solve it now?
anonymous
  • anonymous
hmm..you know how log_b Y = x is equal the y=b^x in exponential form? how could you do that with this equation? isn't that how ur supposed to solve these things?
anonymous
  • anonymous
Yes, but first you have to get \(log_3x\) by itself.
anonymous
  • anonymous
so it's log_3 x = 3c and then 3^3c=x
anonymous
  • anonymous
Nope
anonymous
  • anonymous
whaat???nooo
anonymous
  • anonymous
C(log_3 x) = 3 So you have to divide by C, not multiply
anonymous
  • anonymous
OH. lol...right.
anonymous
  • anonymous
when i solve for (log_5 3)--to conv to exp form, does it still equal to three, which is the what the whole equation is equal to?
anonymous
  • anonymous
No.
anonymous
  • anonymous
That part is trickier
anonymous
  • anonymous
But lets see what you have with C for now.
anonymous
  • anonymous
x=3^3/c
anonymous
  • anonymous
Is that (3^3)/c or 3^(3/c) ?
anonymous
  • anonymous
second one
anonymous
  • anonymous
Correct. Ok, so now to find what C is. \[C = log_5 3 \iff 5^C = 3\]
anonymous
  • anonymous
With me so far?
anonymous
  • anonymous
yep
anonymous
  • anonymous
Ok, so that means that if we take the ln of both sides we get \[C(ln\ 5) = (ln\ 3)\]
anonymous
  • anonymous
polpak i need ur help please
anonymous
  • anonymous
right?
anonymous
  • anonymous
yep
anonymous
  • anonymous
So that means \[C = \frac{(ln\ 3)}{(ln\ 5)}\]
anonymous
  • anonymous
oh~~~
anonymous
  • anonymous
Which means that \[log_53 = \frac{(ln\ 3)}{(ln\ 5)}\]
anonymous
  • anonymous
oh, wow! thanks so much!!
anonymous
  • anonymous
that makes so much more sense now.
anonymous
  • anonymous
Glad I could help.

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