i need it by tomorrow..can you please give the complete solution..?explanation: OPTIONALPr0bLem:e^x-2e^-x=1(read as "e raised to x minus two e raised to negative x equals one")thank you so much..!

__________________
I Love Yahoo! Answers

Solution:1.) Factor out e^x.This becomes: e^x (1 - 2e^-2x) = 12.) Divide both sides by e^x.This becomes: 1 - 2e^-2x = e^-x3.) Transpose the left side to the right side of the equation.This becomes: 2e^-2x + e^-x -1 = 04.) Factor out.This becomes: ( 2e^-x - 1 ) ( e^-x + 1 ) = 05.) Therefore,(equation 1) 2e^-x - 1 = 0(equation 2) e^-x + 1 = 0*********************************We solve equation 1:2e^-x = 1e^-x = 1/2Get ln of both sides:ln(e^-x) = ln(1/2)-x = -ln2So, x = ln 2*******************************Solving equation 2:e^-x = 1Get ln of both sides:ln(e^-x) = ln 1-x = 0So, x = 0***************************The answers are x = ln 2 and x = 0

__________________
I Love Yahoo! Answers