What is the result of logb(B^A)?

To understand why the answer is A, it’s essential to apply the properties of logarithms. The expression logb(B^A) means that we are looking for the exponent that we must raise the base b to in order to obtain B^A.

According to the power rule of logarithms, which states that logb(m^n) = n * logb(m), we can apply this to our case. Here, m is B, n is A, and thus:

logb(B^A) = A * logb(B)

Next, we need to know that logb(B) equals 1. This is because the logarithm of a number to its own base is always 1, meaning b raised to the power of 1 equals B. Therefore, we can simplify:

logb(B^A) = A * 1

logb(B^A) = A

Thus, the result of logb(B^A) simplifies to A, confirming that the answer is indeed A. This principle is fundamental in logarithmic calculations and reinforces the understanding of logarithmic identities.