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Question 19
The number of distinct integer values of n satisfying $$\frac{4-\log_{2}n}{3-\log_{4}n} < 0$$, is
Correct Answer: 47
Solution
Let $$\ \log_2n=y$$
$$\ \ \frac{\ 4-y}{3-\frac{y}{2}}<0$$
$$\ \ \left(4-y\right)\left(3-\frac{y}{2}\right)<0$$
$$\ \ \left(4-y\right)\left(6-y\right)<0$$
$$\ \ \left(y-4\right)\left(y-6\right)<0$$
$$4 < y < 6$$
$$4<\log_2n<6$$
$$2^4<n<2^6$$
$$16<n<64$$
n can take values from 17 to 63(inclusive).
The number of n values possible = 47
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