MTHM 171 Summer Test 4

Logarithms

100

Simplify if Possible

ln(e¹³)

10^log(41)

13

41

200

Find the Domain and range of the following function and tell me a way you could check your answers

f(x)= ln(x+4) - 7

Domain: (-4, infinity)

Range: (-7, infinity)

300

Find the inverse of the following function

f(x)=4^x+5-3

f^-1(x)=log₄(x+3)-5

400

Finish the following statement

As x→∞   y=ln(x)→ _____

As x→∞   y=ln(x)→ ∞

500

If you reflect the graph y=ln(x) across the line y=x, what graph would you obtain?

y=e^x

Exponentials

100

Simplify if possible

e^ln(71)

10^log(31)

71

31

200

Solve

27^4t-1=3^2t

t=3/10

300

Compute the inverse of the following function

f(x)=log₅(2x+4)-6

f^-1(x)=1/2(5^x+6-4)

400

Why does the function e^x have a range of (0,∞)?

☺

500

Solve for the domain of this function

f(x)=log₈((x+2)/(x²-9))

(-3,0)U(3,∞)

Matrices

100

Solve the following system and indicate which method (elimination or substitution) you used

x+y=13
2x-y=2

(5,8)

200

Decode the following matrix

1 0 0  13
0 1 0  2
0 0 1  -14

(13,2,-14)

300

Put in your calculator, decode, and give the answer to the system

1 1 1  10
2 -1 2 11
-1 3 5  32

(2,3,5)

Equations and Inequalities

100

Solve

log(3x-5)=log(7-x)

x=3

200

Solve using a sign diagram
(remember to find zeros and DNEs)

ln(x²-9)<0

(-√10,-3)U(3,√10)

300

Solve

log₄(5x-1)=3

x=13

400

Solve the inequality using a sign diagram

4000(23)^5t ≥ 12000

[(log₂₃(3))/5, ∞)

500

Solve

130/(1+29e^-.9t)=110

t=ln(2/319)/-.9

FUN!!!

100

Solve

-log(x)=log(x)

x=1