Question

Given that 2^x+2^x+2^x+2^x=512, what is the value of x?

I think it simpliflies to 2^4x=512. and 2^9=512 but to get 9 you have to mulitply something to 4, but its 2.25 is that right?

Answer 1

Not quite
(2^x)(2^x)(2^x)(2^x) = 2^(x+x+x+x) = 2^4x

What you have is

2^x+2^x+2^x+2^x = 2^x(1+1+1+1) = 4*2^x = 2^2 * 2^x = 2^(x+2)

So, now you have

2^(x+2) = 2^9
x+2 = 9
x = 7

128+128+128+128 = 512

Answer 2

I don't get how you got 4: 4*2^x = 2^2 * 2^x = 2^(x+2)

Answer 3

Yes Steve you right. there are 4 2^x, which means 4(2^x), which will be 2^2(2^x), then we get the powers we have 2^2 x, thats because when nultiplying numbers with same bases we just add the powers. so will be 2^2 x=2^9. we leave the bases and get the powers and we have 2 x=9, thats x=9-7= 7.