The simplified form of log(75/16) -2 log(5/9) +log(32/243) is ?
2025
The simplified form of log(75/16) -2 log(5/9) +log(32/243) is ?
- A.
log 2
- B.
log 3
- C.
log 1
- D.
log 0
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Solution: simplify using logarithm rules.
Apply the power rule: 2 log(5/9) = log((5/9)^2) = log(25/81).
Combine the logs: log(75/16) - log(25/81) + log(32/243) = log[ (75/16) * (81/25) * (32/243) ].
Simplify stepwise: 75/25 = 3, and 81/243 = 1/3, so the product becomes (3 * 1/3 * 32) / 16 = 32/16 = 2.
Therefore the expression equals log 2.
Answer: log 2