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Exponential and Logarithmic Functions\newlineUsing a graphing calculator to solve an exponential or logarithmic...\newlineUse the ALEKS graphing calculator to solve the equation.\newlinee2−3x=5−3xe^{2-3x}=5-3x\newlineRound to the nearest hundredth.\newlineIf there is more than one solution, separate them with commas.\newlinex=□x=\square

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Q. Exponential and Logarithmic Functions\newlineUsing a graphing calculator to solve an exponential or logarithmic...\newlineUse the ALEKS graphing calculator to solve the equation.\newlinee2−3x=5−3xe^{2-3x}=5-3x\newlineRound to the nearest hundredth.\newlineIf there is more than one solution, separate them with commas.\newlinex=□x=\square
  1. Set up equation: Set up the equation e2−3x=5−3xe^{2-3x} = 5-3x. We need to find the value of xx that satisfies this equation.
  2. Transcendental equation: Since this is a transcendental equation (it involves both an exponential and a linear term), we cannot solve it algebraically using elementary methods. We will use a graphing calculator to find the solution.
  3. Input functions into calculator: Input the left side of the equation, e(2−3x)e^{(2-3x)}, into the graphing calculator as one function (Y1Y_1).
  4. Plot functions on graph: Input the right side of the equation, 5−3x5-3x, into the graphing calculator as another function (Y2Y_2).
  5. Find intersection point: Use the graphing calculator's graphing feature to plot both functions Y1Y_1 and Y2Y_2 on the same set of axes.
  6. Read xx-value from calculator: Use the graphing calculator's intersection feature to find the point(s) where the two graphs intersect. This point(s) will give us the xx-coordinate(s) which is the solution to the equation.
  7. Read xx-value from calculator: Use the graphing calculator's intersection feature to find the point(s) where the two graphs intersect. This point(s) will give us the xx-coordinate(s) which is the solution to the equation.Read off the value of xx from the graphing calculator, rounding to the nearest hundredth as required. If there is more than one solution, note all the xx-values.

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