What will be the solution to: $2^{\cos x}=|x| $Find $x$.

Question

Well, the question is this really.

Find the solution to the eqn. $2^{\cos x}=|x| $

Can it done by plotting on the $\cos$ curve? If we square and take log on both sides, I think we get something similar to $\cos{x} = \log_2{x}$. So $\frac{1}{2} \leq x \leq 2$ ?

Thanks for the help :)

Answer 1

Plot of your functions is

And you get simmetrical solutions for

$$ |x|\approx 1.24686 $$

You can solve such problems easily as you mention or using Wolfram Alpha.

EDIT: the OP need to solve the equation without a plotting tool. In this case you could use the newton's method. It can be done manually and usually it converges quite quickly. You can check it here: WIKIPEDIA LINK

EDIT2: It follows the same plot using functions after having taken the log2 of both functions

Answer 2

You are right, the equation $2^{\cos x}=|x|$ is equivalent to $\cos x = \log_2|x|$, where $\log_2$ is the base-2 logarithm.

But if you want to "solve" (approximate) this by plotting graphs and, you might as well just plot $f(x)=2^{\cos x}$ and $g(x)=|x|$. I see Umberto did just that seconds after I posted this.