Solve the equation \(\displaystyle{e}^{{-{2}{x}+{1}}}={13}\)

jisu61hbke

jisu61hbke

Answered question

2022-03-21

Solve the equation e2x+1=13

Answer & Explanation

armejantm925

armejantm925

Beginner2022-03-22Added 20 answers

Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to perform arithmetic operation on them. Multiplication and division can be written in form of addition and subtraction while operating logarithms.
There are various rules involved in performing logarithmic operations, some required for question are as follows
Product rule logam+logan=logamn
Exponent rule logam=ym=ay
Simplify the expression e2x+1=13 by taking natural log on both sides
ln(e2x+1)=ln(13)
(2x+1)ln(e)=ln(13),(using  ln(am)=mln(a))
2x+1=ln(13),(1)
Solve equation (1) for x to get value of x
2x+1=2.565
2x=2.5651
2x=1.565
x=1.5652
=0.7825
Therefore, value of x is 0.7825

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