SOLUTION: Show that the equation 3sin(e^x) = 2 has a solution between -1 and 0, then solve the equation.

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Question 1057229: Show that the equation 3sin(e^x) = 2 has a solution between -1 and 0, then solve the equation.
Answer by Alan3354(69443) About Me  (Show Source):
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Show that the equation 3sin(e^x) = 2 has a solution between -1 and 0, then solve the equation.
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f(x) = 3sin(e^x) - 2
f(-1) = 3*03596 - 2 = -0.9211
f(0) = 3*0.8415 - 2 = 0.5244
--> crossed the x-axis between -1 and 0.
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3sin(e^x) = 2
sin(e^x) = 2/3
e^x = asin(2/3)
e^x =~ 0.729728
x = ln(0.729728)
x =~ -0.31508