If logx10 + logx2 10 = 10, and if x = 10k, what’s k?
- 1/10
- 1/5
- 3/20
- 2/5
- None of these
Start with x = 10k → 10 = x1/k. Then logx10 = 1/k.
Now, logx210: logx10 = 1/k → x1/k = 10 → (x2)1/2k = 10 → logx210 = 1/2k.
So logx10 + logx210 = 1/k + 1/2k = 10 (given) → 2/2k + 1/2k = 10 → 3/2k = 10
→ 2k = 3/10 → k = 3/20.
The answer is (c).