What is the value of (1/10)log5 1024 — log5 10 + (1/5)log5 3125 ?
2023
What is the value of (1/10)log5 1024 — log5 10 + (1/5)log5 3125 ?
- A.
0
- B.
1
- C.
2
- D.
3
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Solution: Evaluate each logarithmic term and simplify.
(1/10)·log_5(1024) = (1/10)·log_5(2^10) = (1/10)·10·log_5 2 = log_5 2.
-log_5(10) = -log_5(2·5) = -(log_5 2 + log_5 5).
(1/5)·log_5(3125) = (1/5)·log_5(5^5) = (1/5)·5·log_5 5 = log_5 5.
Add the three results: log_5 2 - (log_5 2 + log_5 5) + log_5 5 = 0 (complete cancellation).
Therefore the value of the expression is 0.