Pls help me to solve this problem

[Jason.tuyj]

if 2^x+2^x+2^x+2^x=2^n, what is x in terms of n?

a)n/4
b)4n
c)2n
d)n-2
e)n+2

pls explain

[JohnHarris]

Hi,

You need to try to simplify the equation. First let's work on the left hand side since it looks 'more complicated':
Since
(n*a + n*b + n*c + n*d) = n * (a + b + c + d)
we can start with
2^x + 2^x + 2^x + 2^x = 2^x * ( 1 + 1 + 1 + 1) = 2^x * 4
That is, n is equal to 1 and a, b, c, and d, are all equal to 2^x.

Since 4 = 2^2, we can write this as
2^x * 4 = 2^x * 2^2

Since
a^b * a^c = a^(b+c)
we can finally write
2^x * 2^2 = 2^(x+2)

So what we have now, substituting that last expression into the original left hand side of the equation, is
2^(x+2) = 2^n

The next rule to be used says that if a is neither -1, 0, nor 1 and if
a^u = a^v
then u=v. Thus x+2 = n.

[tim]

Great job, John. To complete the question then, we take John’s x+2 = n to get x = n-2. So the answer is D) n-2..