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STD 11 - 8. sequence and series — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 8. sequence and series4 Marks
MCQ
If $\log _{3} 2, \log _{3}\left(2^{x}-5\right), \log _{3}\left(2^{x}-\frac{7}{2}\right)$ are in an arithmetic progression, then the value of $x$ is equal to $.....$
  • A
    $1$
  • B
    $4$
  • ✓
    $3$
  • D
    $2$
✓

Answer

Correct option: C.
$3$
c
$2 \log _{3}\left(2^{x}-5\right)=\log _{3} 2+\log _{3}\left(2^{x}-\frac{7}{2}\right)$

Let $2^{\mathrm{x}}=\mathrm{t}$

$\log _{3}(t-5)^{2}=\log _{3} 2\left(t-\frac{7}{2}\right)$

$(t-5)^{2}=2 t-7$

$t^{2}-12 t+32=0$

$(t-4)(t-8)=0$

$\Rightarrow 2^{x}=4 \text { or } 2^{x}=8$

$X=2 \text { (Rejected) }$

$\text { Or } x=3$

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