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Answer in Statistics and Probability for eustace kusangwa #90454

Author:
January 24th, 2023

Substitution.

Let “5^x=t, t>0.” Then “5^{2x+1}=5t^2”

“5t^2+4=21t”

“5t^2-21t+4=0”

“D=(-21)^2-4(5)(4)=361”

“t={21pmsqrt {361} over 2(5)}”

“t_1={21-19 over 10}={1 over 5}, t_2={21+19 over 10}=4”

“5^x={1 over 5}=>x=-1”

“5^x=4=>x=log_5(4)={2ln2 over ln5}”

“Big{-1, log_5(4)Big} or Big{-1, {2ln2 over ln5}Big}”

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