The value of log 9/8 - log 27/32 + log3/4 is ?
2023
The value of log 9/8 - log 27/32 + log3/4 is ?
- A.
2
- B.
1
- C.
-2
- D.
zero
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Solution: apply logarithm properties to combine terms.
Step 1: Use subtraction rule for logarithms: log(9/8) - log(27/32) = log((9/8) ÷ (27/32)).
Step 2: Simplify the fraction: (9/8) ÷ (27/32) = (9/8) · (32/27) = 288/216 = 4/3, so the difference equals log(4/3).
Step 3: Add the remaining term: log(4/3) + log(3/4) = log((4/3)·(3/4)) = log(1) = 0.
Answer: 0