Question Statement:
If log_x (5/7) = -1/3, then the value of x is:
Options:
-
(A) 343/125
-
(B) 125/343
-
(C) -25/49
-
(D) -49/25
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2015 Q.5)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: GA
- **Question Type**: **MCQ** (1 Mark)
- **Core Topic**: Quantitative & Analytical Aptitude
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"If log: (5/7) = -1/3, then the value of x is..."*
- **Option (A) [CORRECT]**: *"343/125"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (B) [INCORRECT]**: *"125/343"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (C) [INCORRECT]**: *"-25/49"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"-49/25
Options :
1. V A
2. * B
3. * C
4&D"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **A**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.33 marks).
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