When I enter 2ln(2) - ln(x) = 1 into my calculator I get x=1.472. I get that as an answer no matter how I enter into my calculator. Also, when I plug that into the original equation, the left side equals the right side. However, the text says that the answer should be 10.87 and this is what I get when I solve the equation by hand like so:

2ln(2) - ln(x) = 1

2(e^{ln(2/x}) = e^{1}

4/x = e

x = e*4

x = 10.87

When I plug this into the original equation, the two sides are not equal. What on earth is going on here? :0

I think the text is wrong, and your method too is wrong.

2ln(2) - ln(x) = 1

If you wish to raise them to the power of e, then, all goes up, like this:

e^{2ln(2) - ln(x)}= e^1

e^{ln(4) - ln(x)} = e

e^{ln(\frac4x)}=e

\frac4x = e

x = \frac4e

x = 1.472

This is what I would do though:

2ln(2) - ln(x) = 1

ln(4) - ln(x) = 1

ln(\frac4x)= 1

\frac4x= e^1

x = \frac4e

Oh, that's better. I guess I made the same error as the person who answered the question for the text! Thanks once again! Are you going to be a prof? 'Cause you should be!

Just in case you were wondering, I was using the identity:

If:
log_ab = c

Then;

b = a^c

I don't know... I want to do so many things! :p

Unfortunately, once I get to university, there is practically no going back or I'll lose several years :(

EDIT: Oops, typo... :o

That's great that you have many aspirations. You definitely have a strong understanding of numbers! I'm sure you'll do great at university and whatever you choose to do after that. I heard once that the average person will change careers seven times. University will open so many doors for you. You will likely be able to test out many of your aspirations until you find the one/s that is/are right for you! Good luck, although I'm sure you won't need it!

I made a typing error above that I just saw :o If you'd like to see it again, just in case..

And thanks :)

You're good too, you just need the little push sometimes to get you started. Once you have get to know how to push yourself, I'm sure you'll do well :)

Haha, I was wondering about that! No worries, I make more mistakes than I can count... as I'm sure you've noticed! Lol! And right back at you with the thanks! I have the worst memory when it comes to math... I can get an understanding of something, then, 2 hours later, I forget it! I have a friend who loves math and when she used to help me she would be amazed at how quickly I could forget a concept that I had just recently mastered! So long as I keep trying my best and I have smarty pants people like you and my friend to help me out when I get stuck, I think I'll do all right!:)