algebra help

[annaoh_2003]

Hi, im wondering if someone can explain to me how to solve this equation??

[mabajas76]

So here is the trick, you can assign 2^x a value, lets say t. So 2^2x=t^2, -15x2^x=-15t etc
So you get t^2-15t-16=0, the soloutions for this are t= 16 or -1, using t=16 you get 16=2^x, then 16=2^4 and so x=4.

[Pariz]

Hey - for these types of questions you pretty much wanna reduce it to a simpler quadratic equation.
 
you would let a = 2^x, then substitute into given equation.

so you get

a^2-15a-16=0
(a-16)(a+1)=0
a=16 or a=-1
You ALWAYS reject negatives. resub back to solve for x

2^x=16=2^4
and so x=4

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hope it helped