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Question Number 215232 by Mingma last updated on 01/Jan/25

Answered by devdutt last updated on 01/Jan/25

ln 3(√5) + ln x log _(45) x = 2ln x ⇒ ln 3(√5) + ((ln^2 x)/(ln 45)) = 2ln x ⇒ ln^2 x − 2ln 45 ln x + ln 3(√5) ln 45 = 0 ⇒ ln x = ((2ln 45 ± (√(4ln^2 45 − 4ln 3(√5) ln 45)))/2) = ln 45 ± (√(ln^2 45 − ln 3(√5) ln 45)) ⇒ x = 45e^(±(√(ln^2 45 − ln 3(√5) ln 45))) product of roots = 45^2 = 2025

ln35+lnxlog45x=2lnx⇒ln35+ln2xln45=2lnx⇒ln2x−2ln45lnx+ln35ln45=0⇒lnx=2ln45±4ln245−4ln35ln452=ln45±ln245−ln35ln45⇒x=45e±ln245−ln35ln45productofroots=452=2025

Commented by Mingma last updated on 02/Jan/25

Perfect ��

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