Question 983669
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It is right next to the natural log of 0.5 in the exponent on *[tex \Large e].


Oh! You mean you want me to find the *[tex \Large value] of *[tex \Large x].  Well, you should have asked that in the first place.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3e^{\ln(0.5)x}\ =\ 0.05]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ e^{\ln(0.5)x}\ =\ \frac{0.05}{3}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(e^{\ln(0.5)x}\right)\ =\ \ln\left(\frac{0.05}{3}\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln(0.5)x\ =\ \ln(0.05)\ -\ \ln(3)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\ln(0.05)\ -\ \ln(3)}{\ln(0.5)}]


Is one form of the exact answer.  I'll let you do the calculator work if you need a decimal approximation.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \