Calculus 1000A/B Quiz: Assignment 3 Solutions.pdf

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Chris Brandl

Document Summary

Assignment 3 solutions: solve the following equations for x. (a) e x(cid:113) Notice that this is like a quadratic with respect to e2x. 2 formula we get that the roots are given by e2x = 2x = ln x = ln(cid:0) 1 ln(cid:0) 5. Thus, the two solutions to the equation are x = (b) ln(2ln(x)) = 3 ln(2ln(x)) = 3. 1 (c) ln(x 2e) + ln(x 3e) = 2. We rst simplify the left hand side using properties of logarithms. ln(x 2e) + ln(x 3e) = ln ((x 2e)(x 3e)) Thus, we have that ln (x2 5ex + 6e2) = 2. From this we get x2 5ex + 6e2 = e2 which in turn gives x2 5ex + 5e2 = 0. Now since we need x > 3e for x = ln(x 2e) + ln(x 3e) to be de ned we have the single solution x =