Question

If $\log_{0.3}(x - 1) < \log_{0.09}(x - 1),$ then x lies in the interval

• A. $(2,\infty)$
• B. (– 2, –1)
• C. (1, 2)
• D. None of these

Answer 1

Answer: (A)

$(2,\infty)$

Answer 2

$\log_{0.3}(x - 1) < \log_{(0.3)^{2}}(x - 1) = \frac{1}{2}\log_{0.3}(x - 1)$

$\therefore$1$\frac{1}{2}\log_{0.3}(x - 1) < 0$

or $\log_{0.3}(x - 1) < 0 = \log 1$ or $(x - 1) > 1$or $x > 2$

As base is less than 1, therefore the inequality is reversed, now x>2 $\Rightarrow$x lies in $(2,\infty)$.