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Answer: The two consecutive numbers are 6 and 7.
Step-by-step explanation:
Here the problem is that the logarithm is not the natural logarithm we usually use, to return to the natural logarithm, we can use the next property:
Logₐ(x) = Ln(x)/Ln(a)
Then:
Log₂(75) = Ln(75)/Ln(2)
Now we can do these calculations.
Ln(75)/Ln(2) = 4.317/0.693 = 6.229
Now we want to find two consecutive integers, n and m, such that:
n < 6.229 < m
Because they are consecutive numbers, we must have:
m = n + 1
then:
n < 6.229 < n + 1
The only possibility here is:
n = 6
n + 1 = 7
The two consecutive numbers are 6 and 7.