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Question Number 175443 by Linton last updated on 30/Aug/22

solve for x 16^x +20^x = 25^x

solveforx16x+20x=25x

Answered by Ar Brandon last updated on 30/Aug/22

16^x +20^x =25^x ⇒(((16)/(25)))^x +(((20)/(25)))^x =1 ((4/5))^(2x) +((4/5))^x =1⇒t^2 +t−1=0, t=((4/5))^x t=((−1±(√5))/2)⇒((4/5))^x =(((√5)−1)/2) ⇒x=((ln((√5)−1)−ln2)/(ln4−ln5))

16x+20x=25x⇒(1625)x+(2025)x=1(45)2x+(45)x=1⇒t2+t−1=0,t=(45)xt=−1±52⇒(45)x=5−12⇒x=ln(5−1)−ln2ln4−ln5

Commented by peter frank last updated on 31/Aug/22

thanks

thanks

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