(a)              (b)

Solutions:

(a) divide by 3, take ln, divide by 2:

(b) )

Question 2. Solve for x

(a) 1.04^x = 3 (b) e^0.044x = 6

(c) log(1-x) - log (1+x) = 2 (optional - extra points)

Solutions:

(a) take ln: x ln (1.04) = ln 3, x = ln 3 / ln 1.04 = x = 28.01

(b) take ln: 0.044 x = ln 6, x = ln 6 / 0.044 = x = 40.7218

(c) 

Solve for x: 

(check:  )

Question 3 - Find the inverse function of the following i.e. x = f(y):

(a) y = e^{45x - 1}         (b) y = 

Solutions:

(a) ln y = ln (e^{45x - 1})=45x - 1, 45x = ln(y) + 1,

(b) y = , square both sides: 

Question 4. Solve for x :

(a)          (b) |x - 3| = 7

Solutions:

(a) 10^{log N} = N, so 

So x = 2

(b) |x - 3| = 7, So x-3 = +7 and x-3 = -7 (since abs make both positive 7)

x- 3 = +7 , x = 10

x - 3 = -7, x = -4

So x = -4 or 10

Question 5. Find 2 values of x when the following 2 equations are equal:

y = 10 (2)^x and y = 10 + 15 x

Both equal 10 when x = 0 (y-intercept)

And when graphs intersect at x = 2 (plotting both functions in calculator)