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Previous Year Question (PYQs)

For what value of $x$, the $\log_2(5·2^x+1)$, $\log_4(2^{1-x}+1)$, and 1 are in A.P.?




Solution

Let $a=\log_2(5·2^x+1)$, $b=\log_4(2^{1-x}+1)$, $c=1$ For A.P.: $2b=a+c$ Simplify using $\log_4 y = \frac{1}{2}\log_2 y$ After algebra → $x = 1 - \log_2 5$

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