SOLUTION: Please help me with this problem. Thank You. I don't know where to start with this. Thanks again! 4^-x=1/256

Question 135675: Please help me with this problem. Thank You. I don't know where to start with this. Thanks again!
4^-x=1/256

Answer by nycsharkman(136) (Show Source): You can put this solution on YOUR website!
4^-x=1/256

I would start be rewriting 1/256 as 256^-1. You see, a number raised to a NEGATIVE exponent = the same number raised to a POSITIVE exponent UNDER 1.
So, 256^-1 = 1/256^1 = 1/256.
We now have:
4^-x = 256^-1
We now have to write 256 using a base 4.
Keep in mind that 4^4 = 256.
Then:
4^-x = 4^4
Do you see how we now have the SAME BASE 4 on both sides?
This was our goal.
Since we now have the same base on both sides, simply equate the exponents and solve for x.
-x = 4
x = 4/-1
x = -4
That's it!
Did you follow?

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