Logarithic Function

[flakine]

Logarithic Function:

3 log x=6-2x
10^(6-2x)=x^3

What's my next move?

 

[stapel]

I could be wrong, but I don't think this can be solved algebraically. I think you'd have to use numerical methods to approximate a solution.

Eliz.

 

[tkhunny]

I'd be happy to provide a stronger answer. :roll:

It can't be done using elementary functions. Numerical methods are your only option.

 

[flakine]

What are Numerical methods?

 

[tkhunny]

Fancy words for guessing. Really, "guessing" is a bit glib. Perhaps it would be better to say "guessing with guidance".

The simplest to understand is "Simple Iteration". Solve for ANY variable. In this example, I solved for the 'x' on the Right Hand Side.

x = 3 - (3/2)*log(x)

Now, just pick a value you think might be close to a solution. You can do this by graphing the two sides and just looking at a close guess. I just picked x = 1 out of the air.

Plug this into the right hand side and let the formula tell you what the next guess is. Doing this over and over...

x =
1.00000000
3.00000000
2.28431812
2.46186512
2.41310362
2.42613604
2.42262727
2.42357010
2.42331662
2.42338476
2.42336644
2.42337137
2.42337004
2.42337040
2.42337030
2.42337033
2.42337032
2.42337032

It seems to be settling down. We won't always be so lucky.

Well, there's your introduction to numerical methods. I hope I didn;t scare you too much.

 

[flakine]

Wow, that it! But that's beyond the scope of the section. What gives?

 

[tkhunny]

Wow, that it! But that's beyond the scope of the section. What gives?

Before resorting to numerical methods, I would read over the problem statement VERY CAREFULLY. You are right to be suspicious. Did you write it EXACTLY correctly? Are you expected to respond, "It can't be done?" Maybe it's just wrong as it is writen. It happens.