Finding the Inverse of a Function & Limit of Expression involves Log Function, practice to solve inequalities containing logarithmic function and domain and range of log functions.
A \((-\infty, 2)\cup(5,\infty)\)
B \((-\infty, 6)\cup(10,\infty)\)
C \((-\infty, -4)\cup(4,\infty)\)
D \((2,7)\)
A \(\dfrac {1}{2}\)
B \(-7\)
C 5
D \(0\)
e.g.
In (1) base 2 is greater than 1 whereas in (2) base \(\dfrac {1}{2}\) is less than 1 .
A \(x\in\left (\dfrac {1}{e},\infty\right)\)
B \(x\in(1,e)\)
C \(x\in\left (0,\;\dfrac {1}{e}\right)\)
D \(x\in(e, \infty)\)
For \(a>1\), the graph of \(log_ax\) for different values of \('a'\) will be as shown in figure.
A \(f^{-1}(x)=5^{(5^{x}-6)}\)
B \(f^{-1}(x)=6^{(5^{x}-6)}\)
C \(f^{-1}(x)=7^x\)
D \(f^{-1}(x)=\ell n\,x\)
If \(a>1\), graph of \(\,log_ax\) is
\(\lim\limits_{x\rightarrow\infty}\,log_ax=\infty\) ...(1)
\(\lim\limits_{x\rightarrow0^+}\,log_ax=-\infty\) ...(2)
If \(0<a<1\), graph of \(log_ax\) is:
\(\lim\limits_{x\rightarrow\infty}\,log_ax=-\infty\) ...(3)
\(\lim\limits_{x\rightarrow0^+}\,log_ax=\infty\) ...(4)
A \(\dfrac {5}{3}\)
B 0
C \(-\infty\)
D \(\infty\)