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Sir,
I find these questions really hard to be answered.Hope you can help me solve them.
1)2^(x+4) - 2^(x+2) =3
2)2^(x-1) + 2^(x+1) =320
1) 2^(x+4) - 2^(x+2) = 3.
Factor out 2^x and get 2^x(2^4 - 2^2) = 3.
Note that 2^4 = 16 and 2^2 = 4, and then 16-4=12.
What we have, then, is 2^x(12) = 3.
Dividing both sides by 12 gives us 2^x = 1/4, so x = -2.
2)2^(x-1) + 2^(x+1) = 320.
Again, factor out 2^x and get 2^x(2^-1+ 2^1) = 320.
That is the same as 2^x(1/2 + 2) = 320.
Since 1/2 + 2 is 5/2, we have 2^x(5/2) = 320.
Multiplying both sides by 2/5 gives 2^x = 128.
Now 128 is 2*2*2*2*2*2*2 (that's the product of 7 2's), so x is 7.
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