Olympiads Trick || 3^20 -3^10 || Many Students Really Failed This ||

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[@prollysine]

m+6=log6/log5*(m+5) , m+6=(log6/log5)*m+(log6/log5)*5 , 6-(log6/log5)*5=(log6/log5)*m-m , 6-(log6/log5)*5=m*(log6/log5-1) ,
m=(6-(log6/log5)*5)/(log6/log5-1) , m=~ 3.82747 , test , 5^(m+6)=7.39786*10^6 , 6^(m+5)=7.39786*10^6 , same , OK ,

[@RealQinnMalloryu4]

5^{m+m ➖} +{6+6 ➖ }= 5^{m^2+12}=5^12m^2 60m^2 5^12m^3 5^3^4m^2 5^1^3^4m^2 1^13^2^2m^2 3^1^1m^2 3m^2 (m ➖ 3m+2).
6^{m+m ➖}{ 5+5 ➖ }=6^{m^2+10}=6^10m^2 60m^2 6^10m^2 6^2^5m^2 3^2^1^1m^1 32(m➖ 3m+2).