Math 3 Review #2

Exponential/Logarithmic Conversions

100

e³ = 20.09

ln 20.09 = 3

200

log₃x = 4

3⁴ = x

300

17² = 289

log₁₇289 = 2

400

log 16 = 1.204

10^1.204 = 16

500

19^x = 16

log₁₉ 16 = x

Log Properties

100

Expand log₃ M²N⁶

2log₃ M + 6log₃ N

200

Condense 3ln M - 5ln N

ln (M^3/N^5)

300

Expand log₅ (

(MN^5)/P^8

log₅M + 5log₅ N - 8log₅ P

400

Condense 7ln M - 6ln N + 3ln P

ln((M^7P^3)/N^6)

500

Expand log (7M)²

2log 7 + 2log M

Exponential/Logarithmic Equations

100

e^x = 18

x = 2.89

200

log₃ x = 6

x = 729

300

3^{3x + 6} = 18

x = -1.123

400

ln (x + 8) = 6

x = 395.429

500

Konner has $3500 to invest.  He puts in it in an account that pays 0.5% continuously compounded interest.  How long will it take for Konner to have $4000 in the account?

26.7 years

Writing Polynomial Functions

100

Zeros at 6 and 3

f(x) = x² + 9x + 18

200

Zeros at 0, -2, and 5.

f(x) = x³ + 3x² - 10x

300

Zeros at 8 and 2 + 

sqrt5

f(x) = x³ - 12x² +31x + 8

400

Zero at -5i

f(x) = x² + 25

500

Zeros at -7 + 8i and 2 - 

sqrt15

f(x) = x⁴ + 10x³ + 46x² - 606x - 1243

Number of Possible Zeros

100

Total number of solutions of 

g(x) = 3x⁶ - 5x⁴ + x³ + 16x² - x - 18

6

200

Possible positive real solutions of

g(x) = 3x⁶ - 5x⁴ + x³ + 16x² - x - 18

3 or 1

300

Possible negative zeros of

g(x) = 3x⁶ - 5x⁴ + x³ + 16x² - x - 18

3 or 1

400

Possible number of complex zeros of

g(x) = 3x⁶ - 5x⁴ + x³ + 16x³ - x - 18

0, 2, or 4

500

What are the possible rational zeros for

g(x) = 3x⁶ - 5x⁴ + x³ + 16x² - x - 18

+-1, +-2, +-3, +-6, +-9, +-18, +-1/3, +-2/3

Find Zeros of Polynomial Equations

100

Find zeros of f(x) = x² - 6x - 16

x = -2 and 8

200

Find zeros of g(x) = x² + 3x + 12

x = 

(-3 +-isqrt39)/2

300

g(x) = 2x³ + 20x² - 48x

x = -12 and 2

400

Find zeros of g(x) = x³ - 8x² -21x +108

x = -4, 3, and 9

500

Find the zeros of g(x) = 3x³ + 4x² + 7x - 104

x = 

8/3, -2+-3i