another help with logarithem

[goldgold]

2^(-x)=a-|x|

find in algebraic way for what "a" the equation have

1) no solution
2) one solution
3) two solution
4) three solution

 

[Deleted member 4993]

2^(-x)=a-|x|

find in algebraic way for what "a" the equation have

1) no solution
2) one solution
3) two solution
4) three solution

I would first plot y = 2^(-x) and y = -|x|

And try to investigate what happens when the curve y = -|x| is translated upwards.

That will give you sense under which solutions are possible.

Then you can investigate algebraic way to solve the problem.

Please share your work with us .

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

 

[pka]

\(\displaystyle 2^{-x}=a-|x|\)

find in algebraic way for what "a" the equation have

1) no solution 2) one solution 3) two solution 4) three solution

Not sure what the directions mean.

Note that \(\displaystyle 2^{-x}>0\) so \(\displaystyle a-|x|\le 0\) or \(\displaystyle a\le |x|\).