Question

select the correct answer from each drop - down menu. for all positive values of x, the value of \\(\log_{x}x\\) is always, and the value of \\(\log_{x}1\\) is always.

Explanation:

Step1: Evaluate $\log_x x$

By logarithm definition: if $\log_b a = c$, then $b^c=a$. For $\log_x x$, $x^c=x^1$, so $c=1$.

Step2: Evaluate $\log_x 1$

By logarithm definition: if $\log_b a = c$, then $b^c=a$. For $\log_x 1$, $x^c=x^0$ (since $x^0=1$ for $x>0$), so $c=0$.

Answer:

For all positive values of $x$, the value of $\log_x x$ is always $\boldsymbol{1}$, and the value of $\log_x 1$ is always $\boldsymbol{0}$.