Rules of logarithms

rowe · #1 $Old$ November 6th, 2009, 02:24 AM

Solve for x:

$3x - 2 = e^x$

$ln(3x-2) = x$

At this point, I'm wondering if there's any rule I can apply to $ln(3x-2)$ to get the x term out.

Debsta · #2 $Old$ November 6th, 2009, 03:54 AM

Do you have to solve it algebraically?
If not, you could draw the graph of y = 3x-2 and y = e^x on a GC and find the x-coordinate of where they intersect.

Bacterius · #3 $Old$ November 6th, 2009, 03:57 AM

Solving a logarithmic equation graphically seems a bit of a laugh since the values are highly irrationnal. I can't find a way to solve your equation though ... well its late.

rowe · #4 $Old$ November 6th, 2009, 04:06 AM

"Highly irrational"? I thought there was only one kind, hehe!

Yeah, I'd like an algebraic solution to this. Graphs are for engineers

Defunkt · #5 $Old$ November 6th, 2009, 04:16 AM

Quote:

Originally Posted by rowe $View Post$

"Highly irrational"? I thought there was only one kind, hehe!

Yeah, I'd like an algebraic solution to this. Graphs are for engineers

According to WolframAlpha, this is solved using the Lambert W function.

Are you sure this was the equation you wanted to solve?

HallsofIvy · #6 $Old$ November 6th, 2009, 04:16 AM

Well, there is no "algebraic solution" for this nor, in general, for equations in which the "unknown" appear both inside and outside of a transcendental function. You might be able to write the solution in terms of the Lambert W function (which is defined as the inverse function to $f(x)= xe^x$ but I don't see how offhand.

rowe · #7 $Old$ November 6th, 2009, 04:50 AM

Thanks guys, there must be a mistake with the problem.