Basic Maths and Logarithm
Exponential Equations
JEE Advanced
Grade 11
Question:
If $2^x = 3^y = 6^{-z}$, then $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ equals _____.
Step-by-Step Solution
Key Concept: Let $2^x = 3^y = 6^{-z} = k$. Then $2 = k^{1/x}, 3 = k^{1/y}, 6 = k^{-1/z}$. Since $6 = 2 \cdot 3$: $k^{-1/z} = k^{1/x+1/y} \Rightarrow -1/z = 1/x + 1/y \Rightarrow 1/x + 1/y + 1/z = 0$.
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Correct Answer: 0