Algebra
Logarithms
MMTS_Full_Test_06
Grade 12
Question:
If $\log_{0.3}(x-1)<\log_{0.09}(x-1)$, then $x$ lies in
$(2,\infty)$
$(1,2)$
$(-2,-1)$
None
Step-by-Step Solution
Key Concept: $\log_{0.09}(x-1)=\log_{(0.3)^2}(x-1)=\frac{1}{2}\log_{0.3}(x-1)$
Let $t=\log_{0.3}(x-1)$. $t<t/2\Rightarrow t/2<0\Rightarrow t<0$. $t<0$: $\log_{0.3}(x-1)<0\Rightarrow x-1>1$ (base $<1$: $<0$ means arg $>1$). $x>2$.
Correct Answer: 1