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IPMAT Indore 2019 (MCQ) PYQs

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IPMAT Indore 2019

Modern Math
>
Logarithms

Medium

The inequality log⁡af(x)<log⁡ag(x)\log_{a}{f(x)} < \log_{a}{g(x)} implies that

✅ Correct Option: 1
log⁡af(x)<log⁡ag(x)\log_a f(x) < \log_a g(x) \newline ⇒f(x)>0;g(x)>0\Rightarrow f(x) > 0 ; g(x) > 0
Case - 1 →\rightarrow 0<a<10 < a < 1 \newline ⇒f(x)>g(x)\Rightarrow f(x) > g(x)
Case - 2 →\rightarrow a>1a > 1 \newline ⇒f(x)<g(x)\Rightarrow f(x) < g(x)
\newline The rule states that :- \newline In, log⁡aN<b\log_a N < b \newline N>0,a>0,a≠1N > 0, a > 0, a \neq 1
If 0<a<10 < a < 1 \newline ∴N>ab\therefore N > a^b \\ \newline ⇒\Rightarrow Sign changes
If a>1a > 1 \newline ∴N<ab\therefore N < a^b \\ \newline ⇒\Rightarrow Sign does not change

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