Question

Express y as a function of x. The constant C is a positive number.

ln(y-1)=-6x+lnC

Y=__________

Answer 1

I'm pretty sure there's an =sign somewhere...

Answer 2

sorry just fixed it! thank you for catching it!

Answer 3

Well you want to make it so that y is alone, and, you know... *alone* on one side of the equation. First you'll want to get rid of that nasty "ln" that still tails it... any ideas? :)

Answer 4

Here's a tip..
\[\huge a=b \ \ \rightarrow \ \ e^a=e^b\]

Answer 5

umm instead of ln you would use e ?

Answer 6

No... but we would raise e to both sides of the equation :)
\[\huge \ln(y-1)=-6x+\ln C\]
\[\huge e^{\ln(y-1)}=e^{-6x+\ln C}\]

Answer 7

Ohhh! then how do we get rid of ln from that?

Answer 8

Well, you had best make use of this property
\[\huge e^{\ln b}=b\]

Answer 9

That is to say, raising e to a power, and ln cancel each other out.

Answer 10

okay?

Answer 11

Well? What does that mean for
\[\huge e^{\ln(y-1)}=?\]

Answer 12

will equal to ln(y-1)

Answer 13

I mean y-1

Answer 14

That's right :) So it becomes
\[\huge y -1 = e^{-6x+\ln C}\]
Now, I want you to pay attention to the right side...
What do the laws of exponents say about
\[\huge a^{m+n=?}\]

Answer 15

\[\huge a^{m+n}=a^ma^n\]
right?

Answer 16

yes!

Answer 17

So, the right side may be written
\[\huge y-1=e^{-6x}e^{\ln C}\]

Answer 18

And now we have \(\Large e^{\ln C}\)
What is this equal to?

Answer 19

sorry I have no clue now.

Answer 20

Same with what you did for \(\Large e^{\ln(y-1)}\)

Answer 21

it will equal to C

Answer 22

That's right :)
So finally
\[\huge y-1 =Ce^{-6x}\]
And now, you just have to bring the 1 to the right side, and then y will be alone, as a function of x ^.^

Answer 23

so it would be Y= Ce^-6x +1

Answer 24

Yes it will :)

Answer 25

sorry, I was looking at another question :)

Answer 26

haha its okay thank you a lot!