- Home
- Standard 11
- Mathematics
Basic of Logarithms
medium
If ${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1)$ then $x \ne 1$ lies in
A
$(1, 2)$
B
$(0,1)$
C
($1$, $\infty $)
D
($2$, $\infty )$
Solution
(c) ${\log _{0.3}}(x – 1) < {\log _{0.09}}(x – 1)$
$1 < \frac{{{{\log }_{0.09}}(x – 1)}}{{{{\log }_{0.3}}(x – 1)}}$
==> $1 < {\log _{0.3}}(0.09)$
==> $1 < {\log _{0.3}}{(0.3)^2}$
==> $1 < 2$
Which of true therefore it is true for every positive value of $2$
$\therefore$ $x \in (1,\infty )$.
Standard 11
Mathematics
