1) For x=6 and y?= 4, evaluate each of the following.Round your answers to three decimal places.

a.log(x^y)=

b.(log?  x)^y=

2- Find all numbers x that satisfy the given equation. log5?(x+5)−log5?(x−4)=3

3- Suppose the tuition per semester at Luxim University is $800 plus $750 for each class unit taken.

a. Find a linear function t such that t(u) is the tuition in dollars for a semester in which a student is taking u units.

b. Find a linear function g such that g(s)is the total tuition for a student who takes s semesters to accumulate the 120 units needed to graduate.

4- Suppose your cell phone company offers two calling plans. The pay-per-call plan charges $12 per month plus 4cents for each minute. The unlimited-calling plan charges a flat rate of $28 per month for unlimited calls.

a. What is your monthly cost in dollars for making 700 minutes per month of calls on the pay-per-call plan?

b. Find an equation that gives the cost c in dollars for making m minutes of phone calls per month on the pay-per-call plan.

c. How many minutes per month must you use for the unlimited-calling plan to become cheaper?

If more than ----- minutes per month are used, then the unlimited-calling plan is cheaper.

 

1.

Given x=6 and y?= 4

log(x^y)= log (6⁴) = log (1296) = 3.113

(log? x)^y= [log(6)]⁴ = 4 log(6) since [log (a)]^b = b log(a)

4 log(6) = 4 * 0.77815 = 3.113

2.

log5?(x+5)−log5?(x−4)=3

Here the bases of both equations are same

log5?(x+5) means log ₅ (x+5)

log (a) - log (b) = log(a/b)

So

log₅?(x+5)−log₅?(x−4) = log₅ [(x+5)/(x-4)] = 3

if b^y = x , then log _b (x) = y

Then log₅ [(x+5)/(x-4)] = 3 means 5³ = [(x+5)/(x-4)]

That is

125 = (x+5)/(x-4)

125(x-4) = x+5

125x-500=x+5

124x=505

x=4.0725

3.

Given fee is

$800 plus $750 for each class unit taken.

If class unit taken = u, then

t(u)=800+750*u

b)

Total number of units in s semesters = 120

800 is a fixed charge for one semester

So for s number of semesters, fixed charge will be 800*s

Since 120 units are taken from s number of units, total charge for the units will be 120*750=90000

So the function will be

g(s)=800*s + 90000

4.

Given data

pay-per-call plan charges $12 per month plus 4cents for each minute

unlimited-calling plan charges a flat rate of $28 per month

a) Total calling minutes = 700

if t is the number of minutes called, then cost will be 12 + 0.04*t

So total cost for 700 minutes will be,

12+0.04*700 = 28+12 = 40 dollars

b)

If the number of minutes is m, then cost c will be

c= 0.04*m + 12

c)

Let for m minutes, the charges become equal

That is for m minutes, total cost = 28

So we can write

0.04*m + 12 = 28

0.04m=16

m=400

So if the call minutes is 400, then total charge per month by any plan will be similar

So

If more than 400 minutes per month are used, then the unlimited-calling plan is cheaper.