Question

solve 6e^(2x)=18x^2

Answer 1

u see here
http://www.wolframalpha.com/input/?i=6e%5E%282x%29%3D18x%5E2

Answer 2

Getting the answer from the computer might not convince your math teacher that you know what you are doing, so let's look at this in detail. First, we have to simplify a little.

Answer 3

what do you simplify

Answer 4

\[6e^{2x}=18x^2 \implies e^{2x}=3x^2 \]

Answer 5

Is this for a calculus class?

Answer 6

yeah its calculus summer assign. so i didn't take calc yet

Answer 7

Also, do you use graphing calculators in your class?

Answer 8

yes

Answer 9

the directions for this problem says that you can use calc. i just don't know what to do.

Answer 10

I think you need a graphic solution, or use the computer/calculator to solve.

Answer 11

OK, I'm used to doing it without a calculator, but this one would be really hard that way. Change the statement of the problem to something like this\[e^{2x}=3x^2 \implies f(x)=e^{2x}-3x^2=0\]Plug f(x) into your calculator, and use the graphic or root finding feature to get the value of x that solves.

Answer 12

ok i did. but how do i solve for x?

Answer 13

Your calculator should have a routine that will find the root (zero) of the function. By looking at my TI-84, it seem to be between negative one and zero. You can trace the graph to get an approximation, or there is a solve feature if you know how to use it. You might have to look in the manual.

Answer 14

aaah okay thanks!

Answer 15

My old calculator thinks the answer is about -.391