Question

Solve for all possible values of x: lnx+ln(x-1)=ln6

Answer 1

I guess my main/first question is what does it mean by "for all possible values of x"?

Answer 2

x+x-1=6
2x-1=6
2x=7
x=7/2

Answer 3

that doesn't seem right... how can i just ignore the ln stuff?

Answer 4

You take everyting to the power of e

Answer 5

It's just a fancy way of saying `solve for x`. :)
Yah there's a small mistake in there smart.
We first need to write the left side as a single logarithm.

Answer 6

Oh, shoot. I am really tired tonight

Answer 7

ln(x^2-x)=ln6

Answer 8

oh so just multiply by e on both sides and then solve? seems too easy

Answer 9

Here's a helpful rule of logarithms.\[\large \log a+\log b=\log (ab)\]
You can use this rule to write the left side as a single logarithm.

Answer 10

oh so then i just multiply by e on both sides to get rid of the ln and then solve?

Answer 11

AFTER you've done that, yes you can "exponentiate" both sides, write them with a base of e.
And the logs/e's will "disappear"! poof!

Answer 12

Yes, but there is one thing to be careful about!!

Answer 13

After you solve for x, (you should get 2 values, since you have a quadratic), you'll want to plug both of those values back into the original problem to make sure they're in the domain of the function!

If for example one solution is x=-2.

\(ln(-2-1)\) doesn't exist! So we wouldn't include that solution.

Answer 14

oh ok thanks. So when i'm showing my work, how exactly would I write the step where i get rid of the lns?