Question

The domain of the function defined by $f(x)=log_x 10$ is:

• A. $x<10$ excluding $x = -10$
• B. $x>10$
• C. $x \ge 10$
• D. $x>0$ excluding $x = 1$

Hint:

Log base $b$: $b>0$ and $b \neq 1$.

Answer 1

The Correct Option is D

Step 1: Concept
For a logarithm $log_b a$ to be defined, the base $b$ must be positive ($b>0$) and not equal to 1 ($b \neq 1$).
Step 2: Analysis
In $f(x) = log_x 10$, the variable $x$ is the base.
Condition 1: $x>0$
Condition 2: $x \neq 1$
Step 3: Conclusion
The domain is $x \in (0, \infty) \setminus \{1\}$. Final Answer:(D)