How do I solve for xx? 2e^{2x}-5e^x-3=02e2x−5ex−3=0 This problem is about the natural logarithm function. Algebra Quadratic Equations and Functions Linear, Exponential, and Quadratic Models 1 Answer Cesareo R. Jun 9, 2016 x = log_e3x=loge3 Explanation: Making e^x = yex=y and substituting we have the equivalent problem. 2 y^2-5y-3=02y2−5y−3=0 Solving for yy gives y = {-1/2,3}y={−12,3} we take the consistent one which is y = 3 = e^xy=3=ex because e^x > 0 forall x in RR and solving for x gives x = log_e3 Answer link Related questions What is the linear regression line? How do you determine if the following data set is linear or quadratic: (-4,10), (-3,7), (-2,4),... How do you know if the following data set is exponential: (0,120), (1, 180), (2, 270), (3, 405)? How do you use the graphing calculator to find the linear regression line? How do you find the best function that models: (-3, 14), (-2, 4), (-1, -2), (0, -4), (1, -2)? If the same amount is added to one dimensions and removed from the other, the resulting... A child care center has 440 feet of fencing to enclose two adjacent rectangular safe play areas.... How do you write the quadratic equation of the graph with the given points (-3, 4), (1,0), and (-1,-2)? A painter is making a rectangular canvas for her next painting. She wants the legnth of the... Is f(x)= 3x^2 an exponential function? See all questions in Linear, Exponential, and Quadratic Models Impact of this question 7516 views around the world You can reuse this answer Creative Commons License