Solve for x Do not use a calculator a 4x 2 7 b xe2x xex1S

Solve for x. Do not use a calculator.

a. 4^x + 2 = 7

b. xe^2x = x^ex+1

Solution

a)

4x+2=7

4x= 7-2=5

x=5/4 = 1.25

b)

xe2x = xex+1

xe2x - xex=1

xe^x(e^x-1)=1

Take natural log both sides

ln(x) + x + ln( e^x-1)=0

x= - ln(x(e^x-1))