Chapter 6 Jeopardy Review

Rewriting

100

Rewrite the following expression in its equivalent exponential form:

4 = log_x16

x⁴ = 16

200

Rewrite the following expression in its equivalent logarithmic form:

y⁵ = 96

log_y96 = 5

300

Write the expression as a single logarithm and solve:

log₃6 + log₃8

log₃48 = 3.52

400

Write the expression as a single logarithm and solve:

3log2 + log4

log32 = 1.51

500

Expand the logarithm:

log_8((12x^5)/(y))

log₈12 + 5log₈x - log₈y

Evaluating

100

Evaluate the following expression:

9^log₉⁴⁵

45

200

Evaluate the expression:

log₂10

3.32

300

Evaluate the expression:

log₂₃42

1.19

400

Evaluate the expression:

log₄4^5x

5x

500

Evaluate the expression:

ln(1.6)

.47

Solving

100

Solve the equation:

2^2x = 16

2

200

Solve the equation:

log₃(75 - 3x) = 2

22

300

An investment of $25,000 for 6 years at an interest rate of 4% if it is compounded monthly.

$31,768.55

400

An investment of $25,000 for 6 years at an interest rate of 4% if it is compounded continuously.

$31,781.23

500

An investment of $10,000 for 5 years at an interest rate of 4.5% if it is compounded semiannually.

$12,492.03

Graphing

100

Determine if this is an exponential growth or decay and explain why:

y = 2(1.5)^x

Growth - 1.5 is bigger than 1

200

Graph the original and the transformation:

f(x) = log₃x          g(x) = log₃(x - 2) + 1

Right 2 up 1

300

Graph the original and its transformation:

f(x) = 3^x         g(x) = 3^x-2+1

Right 2 up 1

400

Determine the type of function from the table:

x | 1 | 3 | 5 | 7 | 9 |

y |81|27| 9 | 3 | 1 | 

Exponential

500

Determine if the data is an exponential relationship. Then write the function that models the data.

x |-4|-2| 0 |  2  |   4  |

y | 6|24|96|384|1536|

Exponential

y = 96(2)^x

Simplifying

100

Simplify:

(20e⁴)/(4e³)

5e

200

Simplify:

log₃9^x

2x

300

Simplify:

(4e^3x)²

16e^6x

400

Simplify:

2log₂x + 5log₂2 - log₂8

log_2((32x)/8)

500

Simplify:

6ln(2) - 4ln(y)

ln (64/(y^4))