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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{5^x-4^x}{4^x-3^x}$ is equal to
  • A
    $0$
  • ✓
    $\frac{\log \left(\frac{5}{4}\right)}{\log \left(\frac{4}{3}\right)}$
  • C
    1
  • D
    $\log \left(\frac{5}{4}\right)$
✓

Answer

Correct option: B.
$\frac{\log \left(\frac{5}{4}\right)}{\log \left(\frac{4}{3}\right)}$
(B)
$\lim _{x \rightarrow 0} \frac{5^x-4^x}{4^x-3^x}=\lim _{x \rightarrow 0} \frac{\left(\frac{5^x-1}{x}\right)-\left(\frac{4^x-1}{x}\right)}{\left(\frac{4^x-1}{x}\right)-\left(\frac{3^x-1}{x}\right)}$
$=\frac{\log 5-\log 4}{\log 4-\log 3}$
$=\frac{\log \left(\frac{5}{4}\right)}{\log \left(\frac{4}{3}\right)}$

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