Find the value of log (a2/bc) + log (b2/ac) + log (c2/ab) ?
2024
Find the value of log (a2/bc) + log (b2/ac) + log (c2/ab) ?
- A.
1
- B.
zero
- C.
-1
- D.
-2
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Solution: Use logarithm properties to expand and simplify the expression.
Apply rules: log(x/y)=log x - log y and log(x^2)=2 log x.
Expand each term: log(a^2/bc) = 2 log a - log b - log c; log(b^2/ac) = 2 log b - log a - log c; log(c^2/ab) = 2 log c - log a - log b.
Add the three expressions and group like terms: (2 log a - log b - log c) + (2 log b - log a - log c) + (2 log c - log a - log b) = (2 log a - log a - log a) + (2 log b - log b - log b) + (2 log c - log c - log c) = 0 + 0 + 0 = 0.
Answer: 0