Inverting the exponential decay equation? How would I algebraically isolate x in the following exponential decay equation, so that x is most easily derived? y = A e^(-lambda x)

reevelingw97

reevelingw97

Answered question

2022-11-19

Inverting the exponential decay equation?
How would I algebraically isolate x in the following exponential decay equation, so that x is most easily derived?
y = A e λ x

Answer & Explanation

Zoey Benitez

Zoey Benitez

Beginner2022-11-20Added 18 answers

Apply log on both sides :
log ( y ) = log ( A e λ x ) = log ( A ) + log ( e λ x ) = log ( A ) λ x log ( e ) = log ( A ) λ x .
Therefore (if λ 0) we got
x = log ( A ) log ( y ) λ

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