Manhattan GMAT Question
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DanaJ
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4^4x means 4 raised to the 4x-th power, which cannot be 1600. Doing the prime factorization of 1600 you get that it is equal to (4^3)*(5^2), so it cannot be a power of 4. Therefore IMHO your equation is not correctly written.
This can be solved:
4^4x = 2^8x and 1600 = 40^2 = (5^2)*(2^6) , therefore
2^8x=(5^2)*(2^6) Multiply both with the power 1/2
2^4x= 5 * 2^3 Thus 2^4x = 40 ---> a
Now we are looking for (4^x–1)^2 which is = 2^4x-4
2^4x-4 = 2^4x * 1/16 Now sustitute with a
40 * 1/16 = 5/2
4^4x = 2^8x and 1600 = 40^2 = (5^2)*(2^6) , therefore
2^8x=(5^2)*(2^6) Multiply both with the power 1/2
2^4x= 5 * 2^3 Thus 2^4x = 40 ---> a
Now we are looking for (4^x–1)^2 which is = 2^4x-4
2^4x-4 = 2^4x * 1/16 Now sustitute with a
40 * 1/16 = 5/2
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sureshbala
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Folks, this was answered earlier....Here is the link
https://www.beatthegmat.com/exponents-pr ... tml#123429
https://www.beatthegmat.com/exponents-pr ... tml#123429
