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Sequences and Series question

2020 · Shift 1 · Q31
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  5. /2020 · Shift 1 · Q31

Sequences and Series question

2020 · Shift 1 · Q31

JEE AdvancedMathematicsSequences and SeriesNumerical+4 / −1
Let m be the minimum possible value of log⁡3(3y1+3y2+3y3){\log _3}({3^{{y_1}}} + {3^{{y_2}}} + {3^{{y_3}}})log3​(3y1​+3y2​+3y3​), where y1,y2,y3{y_1},{y_2},{y_3}y1​,y2​,y3​ are real numbers for which y1+y2+y3{{y_1} + {y_2} + {y_3}}y1​+y2​+y3​= 9. Let M be the maximum possible value of (log⁡3x1+log⁡3x2+log⁡3x3)({\log _3}{x_1} + {\log _3}{x_2} + {\log _3}{x_3})(log3​x1​+log3​x2​+log3​x3​), where x1,x2,x3{x_1},{x_2},{x_3}x1​,x2​,x3​ are positive real numbers for which x1+x2+x3{{x_1} + {x_2} + {x_3}}x1​+x2​+x3​= 9. Then the value of log⁡2(m3)+log⁡3(M2){\log _2}({m^3}) + {\log _3}({M^2})log2​(m3)+log3​(M2) is ...........
Numerical answer
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