After solving this, exponential equation I get two answers for x, my question is are both he values valid? Or is any one value valid?

Question

After solving this, exponential equation I get two answers for x, my question is  are both he values valid? Or is any one value valid?

anonymous · Answer

depends on the equation and your solution.

anonymous · Answer

$$4^{x ^{2}-6} - 16 ^{x+1}$$

anonymous · Answer

This is not an equation.

anonymous · Answer

sorry by mistakenly put - instead of = @FoolForMath

anonymous · Answer

@ash2326 Need help!

anonymous · Answer

^^^ The whole expression equal to zero.

saifoo.khan · Answer

call 15 for help.

saifoo.khan · Answer

$$\Large 4^{x^2 - 6} - 4^{2(x+1)} = 0$$

anonymous · Answer

^ Yes I know my question is After solving this, exponential equation I get two answers for x, my question is  are both he values valid? Or is any one value valid?

anonymous · Answer

Okay then $$ x^2 - 6 = 2x+2 \implies x= -2\; or \; x=-4 $$

saifoo.khan · Answer

Try inserting them back in the place of "x" one by one.

anonymous · Answer

@saifoo.khan But that can be time consuming, (specially in SAT, where you're bound in terms of time) ...

anonymous · Answer

I just want to ask Whenever you get such type of exponential equation to solve, and you get two answers for x, are both valid? Or how to determine ?

saifoo.khan · Answer

No. 
like let's say you get 2.

insert 2 back in there and if you get that equal to 0.. then it means the solution is correct.

anonymous · Answer

Or say you have something with $ e^x $ here x>0 (always). I can't think of any thing bad happening other wise.

anonymous · Answer

Rephrasing my earlier comment, if for instance you get an imaginary root while solving the quadratic then that is to be eliminated.

ash2326 · Answer

@Zeerak you understood?