e2x2exSolutionWe have e2x 2ex Let ex a Then a2 2a or a2

e^(2x)=2e^(x)

Solution

We have e^2x = 2e^x . Let e^x = a. Then, a² = 2a or a² -2a = 0 or a(a -2 ) = 0. Thus either a = 0 or a = 2.

When e^x = 0 , then x = - . Also, when e^x = 2, we have, on taking natural logarithm of both the sides, x ln e = ln 2 or, x = ln 2 ( as ln e = 1) or x = 0.693147718 (approximately) = 0.69 ( on rounding off to 2 decimal places).