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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = {2^{1/{{\log }_x}4}}$, then $ x$  is equal to
  • A
    $\sqrt y $
  • B
    $y$
  • ✓
    ${y^2}$
  • D
    ${y^4}$
✓

Answer

Correct option: C.
${y^2}$
c
(c) Given $y = {2^{1/{{\log }_x}4}} \Rightarrow \log y = \frac{1}{{{{\log }_x}4}}(\log 2)$

$ \Rightarrow {\log _x}4 = \frac{{\log 2}}{{\log y}} $

$\Rightarrow \frac{{{{\log }_e}4}}{{{{\log }_e}x}} = \frac{{{{\log }_e}2}}{{{{\log }_e}y}} $

$\Rightarrow \frac{{2\log 2}}{{\log x}} = \frac{{\log 2}}{{\log y}}$

==> $2\log y = \log x \Rightarrow x = {y^2}$.

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