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Difficulty:
25%
(medium)
Question Stats:
81% (01:49) correct
19%
(02:23)
wrong
based on 192
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If \(\frac{(2^x)(7^y)}{14^5}\) = \(98^3\), then \(x + y\) =
1. 11
2. 14
3. 15
4. 19
5. 20
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1. 11
2. 14
3. 15
4. 19
5. 20
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Abhishek009
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Posts: 5,879
AkshdeepS
\(98 =7^2*2\)
So, \(98^3 =7^6*2^3\)
Agin, \(\frac{(2^x)(7^y)}{14^5}\) = \(7^6*2^3\)
Or, \(\frac{(2^x)(7^y)}{7^5*2^5}\) = \(7^6*2^3\)
Or, \((2^x)(7^y)\) = \(7^{11}*2^8\)
So, \(x = 8\) and \(y = 11\)
Thus, \(x + y = 19\) , Answer must be (4)
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Solution
Given:
- • \(\frac{(2^x)(7^y)}{14^5}\) = \(98^3\)
To find:
- • The value of (x + y)
Approach and Working:
If we simplify the given expression, we get
- • \(\frac{(2^x)(7^y)}{14^5}\) = \(98^3\)
Or, \(\frac{(2^x)(7^y)}{(2^5)(7^5)}\) = \(2^3 * 7^6\)
Or, \((2^{x-5})(7^{y-5})\) = \(2^3 * 7^6\)
Comparing both sides of the equation, we get
- • (x – 5) = 3
Or, x = 8
- • (y – 5) = 6
Or, y = 11
- • Hence, (x + y) = 8 + 11 = 19
Hence, the correct answer is option 4(D).
Answer: 4(D)
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