Subjects algebra

Log Reciprocal E9Fa5D

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1. Problem statement: Determine the correct expression among the options for $\log_a x$. 2. Formula: Use the change of base formula. $$\log_a x = \frac{\ln x}{\ln a}$$ 3. Important rule: For $a>0$, $a\neq 1$ and $x>0$ the change of base gives a reciprocal relation between $\log_a x$ and $\log_x a$. $$\log_x a = \frac{\ln a}{\ln x}$$ 4. Intermediate work: Taking the reciprocal of $\log_x a$ yields $$\frac{1}{\log_x a} = \frac{\ln x}{\ln a}$$ 5. Conclusion: Therefore $\log_a x = \frac{1}{\log_x a}$ and the correct choice is C. 6. Final answer: C) 1/(Log_x a).