What is the value of m m in the equation below?
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- MartyMurray
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On the left side of the equation in the denominators you have a prime, 5, and a square of a prime, 4.
On the right side you have 2, a prime, and 10, a non prime.
Try factoring the denominators into primes and seeing where that takes you.
On the right side you have 2, a prime, and 10, a non prime.
Try factoring the denominators into primes and seeing where that takes you.
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Every prime factor on the right side must also appear on the left side.
On the right side we have 1/10�� = 1/2�� * 1/5��.
Thus, the left side must also include 1/5��, implying that m=47.
The correct answer is D.
On the right side we have 1/10�� = 1/2�� * 1/5��.
Thus, the left side must also include 1/5��, implying that m=47.
The correct answer is D.
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(1/5)^m x (1/4)^24 = 1/(2(10)^47)
(1/4)^24 can be rewritten in its equivalent form of (1/2)^48.
Now we have (1/5)^m x (1/2)^48 = 1/(2(10)^47).
So on the right side of the equation we have 47 factors of 10 in the denominator and one leftover 2.
Hence m must equal 47.
(1/5)^47 x (1/2)^48 would yield 47 factors of 10 and one leftover 2.
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You can also crossmultiply. That gives
2 * 10�� = 5� * 4²�
which is much easier for most students to solve.
2 * 10�� = 5� * 4²�
which is much easier for most students to solve.
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It is very informative and easy to solve when we use simplified solution like this
cross multiplication
2 * 10�� = 5� * 4²�
cross multiplication
2 * 10�� = 5� * 4²�
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Simplifying the equation, we have:
1/(5^m) * 1/(4^24) = 1/[2(10)^47]
1/(5^m * 2^48) = 1/[2(2^47 * 5^47)]
5^m * 2^48 = 2^48 * 5^47
5^m = 5^47
m = 47
Answer: D
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