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Logarithm question

2023 · 25 Jan · Shift 1 · Q43

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PYQ Library
JEE Main
Mathematics
Logarithm
2023 · 25 Jan · Shift 1 · Q43

Logarithm question

2023 · 25 Jan · Shift 1 · Q43

JEE MainMathematicsLogarithmNumerical+4 / −1

Let

S = \left\{ {\alpha :{{\log }_2}({9^{2\alpha - 4}} + 13) - {{\log }_2}\left( {{5 \over 2}.\,{3^{2\alpha - 4}} + 1} \right) = 2} \right\}

. Then the maximum value of

\beta

for which the equation

{x^2} - 2{\left( {\sum\limits_{\alpha \in s} \alpha } \right)^2}x + \sum\limits_{\alpha \in s} {{{(\alpha + 1)}^2}\beta = 0}

has real roots, is

\underline{\hspace{2cm}}

.

Numerical answer

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