Between what two consecutive integers does log ₂ 75 lie?

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.

answer: 1 + 1 = 11

step-by-step explanation:

find the vertical and horizontal asymptotes of the function f x = 5 x − 1 . to find the vertical asymptote, equate the denominator to zero and solve for . since the degree of the polynomial in the numerator is less than that of the denominator, the horizontal asymptote is .

step-by-step explanation: