6 Solve the following equations Show all work Place your fin

6. Solve the following equations. Show all work. Place your final answer in dhe space provided in complete form (a) 201 =5 (b) 2e-3e5 o (log,()+ log2(x)-3 9:20 PM dd) 11/22/2017

Solution

a) 20 (1/2)^x = 5

dividing both sides by 20

1/2 ^x = 1/4

(1/2)^x = (1/2)^2

x = 2

b) 2e^x - 3e^-x =-5

let e^x = y

2y - 3/ y = -5

2y^2 - 3 = -5y

2y^2 + 5y - 3 = 0

( y +3 ) ( 2y - 1) = 0

y = -3 , y = 1/2

discarding negative value

e^x = 1/2

x ln e = ln 1/2

x = ln 1/2

x = -0.693