Question

Which of the following pairs are not equivalent statements?

A x = √y and x = y^1/2
B log N = B and B = N
C ln(x) = y and x = e^y
D log_b N = p and b^p

Answer 1

Statement B (log N = B and B = N) is not equivalent because it should be 10^B = N to be correct. Similarly, Statement D (log_b N = p and b^p) is missing the equivalent comparison for N; it needs to be N = b^p.

Step-by-step explanation:

The pairs of statements which are not equivalent are as follows:

• A: x = √y and x = y^1/2

• B: log N = B and B = N

• C: ln(x) = y and x = e^y

• D: log_b N = p and b^p

Statement A is equivalent because √y is the same as raising y to the power of 1/2. Statement C is also equivalent because the natural logarithm ln(x) is the inverse function of e^y, meaning if ln(x) = y, then x = e^y. However, statement B is not equivalent because log N = B means that 10^B = N, not B = N. And statement D is missing a comparison for B; it should be log_b N = p and N = b^p to be equivalent.