Question

Which of the following is equivalent to log(a) * log_a(5)?

A) log(a)
B) log(5)
C) log(5a)
D) log_a(5a)

Answer 1

The expression log(a) * log_a(5) simplifies to log(a) because log_a(5) is equivalent to 1, resulting in the multiplication by log(a) being unaffected.

Step-by-step explanation:

The question involves the concept of logarithms and their properties. When we are given log(a) * loga(5), we are dealing with a property where the logarithm of the number with its own base results in 1 (because any number to the power of 0 equals 1, and loga(a0) = 0). Therefore, loga(5) is equivalent to 1 when multiplied by log(a), which gives us:

log(a) * loga(5) = log(a) * 1 = log(a)

Thus, the equivalent expression to log(a) * loga(5) is log(a), which makes the answer (A) log(a).