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For integers x and y, 25^(10)*100^x=2^y. What is the value of y?
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01 Apr 2022, 02:24
01 Apr 2022, 02:24
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For integers x and y, \(25^{(−10)}*100^x=2^y\). What is the value of y?
A. -10
B. 10
C. 20
D. 25
E. 40
A. -10
B. 10
C. 20
D. 25
E. 40
Re: For integers x and y, 25^(10)*100^x=2^y. What is the value of y?
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01 Apr 2022, 03:17
01 Apr 2022, 03:17
1
\(25^{(−10)}*100^x=2^y\)
\(5^{-20} * 2^{4x} * 5^{4x} = 2^y * 5^0\)
Comparing the powers of bases
\(4x - 20 = 0\)
\(x = 5\)
\(2^{4x} = 2^y\)
\(y = 4x = 20\)
Answer \(C\)
\(5^{-20} * 2^{4x} * 5^{4x} = 2^y * 5^0\)
Comparing the powers of bases
\(4x - 20 = 0\)
\(x = 5\)
\(2^{4x} = 2^y\)
\(y = 4x = 20\)
Answer \(C\)
Re: For integers x and y, 25^(10)*100^x=2^y. What is the value of y?
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01 Apr 2022, 10:56
01 Apr 2022, 10:56
1
25^-10 * (4*25)^x
To cancel 25 from num & denominator, x needs to be 10 ---> 4^10 ----> 2^2*10 ----> 2^20
Hence y = 20 and ans is option C
To cancel 25 from num & denominator, x needs to be 10 ---> 4^10 ----> 2^2*10 ----> 2^20
Hence y = 20 and ans is option C
