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?
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
I don't get how you got 4: 4*2^x = 2^2 * 2^x = 2^(x+2)
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.
To solve the equation 2^x + 2^x + 2^x + 2^x = 512, you can start by combining the terms on the left side:
4 * 2^x = 512
Now, to isolate 2^x, divide both sides of the equation by 4:
(4 * 2^x) / 4 = 512 / 4
This simplifies to:
2^x = 128
Now, you can rewrite 128 as a power of 2, since 2^7 equals 128:
2^x = 2^7
Since the bases are equal, the exponents must also be equal:
x = 7
So, the value of x that solves the equation is 7.