Question

If (log_3 X) (log_5 3) = 3, find x

Answer 1

Which one of these has an x?

Answer 2

The other one is just a multiplicative constant. You can divide it over to the other side.

Answer 3

?? how? the bases are diff-- three and five...how can u just divide?

Answer 4

Because the log base 5 of 3 is just a number. Like 4/5 or the square root of 15

Answer 5

=( i still don't get it....

Answer 6

Ok here. Lets say that \[C=log_5 3\]

Now your equation looks like:
\[C(log_3 x) = 3\]

Can you solve it now?

Answer 7

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?

Answer 8

Yes, but first you have to get \(log_3x\) by itself.

Answer 9

so it's log_3 x = 3c and then 3^3c=x

Answer 10

Nope

Answer 11

whaat???nooo

Answer 12

C(log_3 x) = 3

So you have to divide by C, not multiply

Answer 13

OH. lol...right.

Answer 14

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?

Answer 15

No.

Answer 16

That part is trickier

Answer 17

But lets see what you have with C for now.

Answer 18

x=3^3/c

Answer 19

Is that (3^3)/c or 3^(3/c) ?

Answer 20

second one

Answer 21

Correct.
Ok, so now to find what C is.

\[C = log_5 3 \iff 5^C = 3\]

Answer 22

With me so far?

Answer 23

yep

Answer 24

Ok, so that means that if we take the ln of both sides we get

\[C(ln\ 5) = (ln\ 3)\]

Answer 25

polpak i need ur help please

Answer 26

right?

Answer 27

yep

Answer 28

So that means \[C = \frac{(ln\ 3)}{(ln\ 5)}\]

Answer 29

oh~~~

Answer 30

Which means that
\[log_53 = \frac{(ln\ 3)}{(ln\ 5)}\]

Answer 31

oh, wow! thanks so much!!

Answer 32

that makes so much more sense now.

Answer 33

Glad I could help.