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8. Sequences and Series
normal
જો ${\log _5}2,\,{\log _5}({2^x} - 3)$ અને ${\log _5}(\frac{{17}}{2} + {2^{x - 1}})$ એ સમાંતર શ્રેણી માં હોય તો $x$ ની કિમત મેળવો
A
$0$
B
$-1$
C
$3$
D
$4$
Solution
$2 \mathrm{b}=\mathrm{a}+\mathrm{c}$
$\Rightarrow 2 \log _{5}\left(2^{\mathrm{x}}-3\right)=\log _{5} 2+\log _{5}\left(\frac{17}{2}+2^{\mathrm{x}-1}\right)$
$\Rightarrow\left(2^{\mathrm{x}}-3\right)^{2}=2\left(\frac{17}{2}+2^{\mathrm{x}-1}\right) \Rightarrow 2^{2 \mathrm{x}}-7.2^{\mathrm{x}}-8=0$
$\Rightarrow \mathrm{x}=3$
Standard 11
Mathematics
