If 4^4x = 1600, what is the value of [4^(x–1)]^2?
40
20
10
5/2
5/4
exponents
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For questions like this, I think it makes sense not to solve for x.
from here we have:
4^4x = 1600 (Equation 1)
Now lets take a ratio of what we have vs. whats required:
4^4x / [4^(x–1)]^2 = 4 ^ (2x + 2) (Ratio 1)
From Equation 1, 4^2x = 40
Thus 4^(2x+2) = 40 * 16 = 640
So what we need now is 1600/640 (from Ratio 1)
This simplifies to 5/2
is that correct?
from here we have:
4^4x = 1600 (Equation 1)
Now lets take a ratio of what we have vs. whats required:
4^4x / [4^(x–1)]^2 = 4 ^ (2x + 2) (Ratio 1)
From Equation 1, 4^2x = 40
Thus 4^(2x+2) = 40 * 16 = 640
So what we need now is 1600/640 (from Ratio 1)
This simplifies to 5/2
is that correct?
let's work with 1600 first
1600= 4^2 * 100
1600=4^2 * 4*25
1600=4^3 * 25
since 25 is just above 16 we can say 4^3 * 4^2.1=1600
so, 4^5.1 =1600
now back to the orig: 4^4x=1600
x= 5.1/4
pug x into 2nd equation
[4^(x–1)]^2
(4^1/4)^2
4^1/4 is the same as sqrt root of 2=
ans =2
since we approximate the answer is 2 something, D, 5/2
1600= 4^2 * 100
1600=4^2 * 4*25
1600=4^3 * 25
since 25 is just above 16 we can say 4^3 * 4^2.1=1600
so, 4^5.1 =1600
now back to the orig: 4^4x=1600
x= 5.1/4
pug x into 2nd equation
[4^(x–1)]^2
(4^1/4)^2
4^1/4 is the same as sqrt root of 2=
ans =2
since we approximate the answer is 2 something, D, 5/2
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Suddenly I stumbled upon an explanation of my own...here goes..
4^4x = 1600; we have to find [4^(x-1)]^2
[4^(x-1)]^2 = 4^(2x-2) [multiplication law of exponents]
Now if we square this we get --- [4^(2x-2)]^2
= 4^(4x-4)
= 4^4x/4^4 (Again using law of exponents)
= Now we know that 4^4x = 1600
Hence 4^4x/4^4 = 1600/16*16 = 25/4
Now [4^(2x-2)]^2 = 25/4
Hence sqr rt of this or [4^(2x-2)] = sqr rt of (25/4) = 5/2
Yippie...I solved it too!
4^4x = 1600; we have to find [4^(x-1)]^2
[4^(x-1)]^2 = 4^(2x-2) [multiplication law of exponents]
Now if we square this we get --- [4^(2x-2)]^2
= 4^(4x-4)
= 4^4x/4^4 (Again using law of exponents)
= Now we know that 4^4x = 1600
Hence 4^4x/4^4 = 1600/16*16 = 25/4
Now [4^(2x-2)]^2 = 25/4
Hence sqr rt of this or [4^(2x-2)] = sqr rt of (25/4) = 5/2
Yippie...I solved it too!