Ch 6 Review: Exp & Log Fcns

Growth & Decay

100

Sketch f(x) = 2^x - 4 and state the asymptote and y-intercept.

HA: y = -4

y-int: (0, -3)

200

The population of a large city was about 4.6 million in the year 2010 and grew at a rate of 1.3% for the next 4 years. What exponential function models this situation?

P = 4.6(1.013)^t

300

Tom buys car for $40,300. It depreciates in value at a rate of 17% each year. What is the value of the car after 5 years. 

$15,874.33

400

Joe deposited $11,600 in an account that pays 1.75% interest. Find the balance after 3 years if the interest is compounded quarterly.

$12,223.87

500

Olivia has inherited land from her grandma. She decided the sell the land for $130,000 then place the money in a new account that earns 1.8% interest compounded monthly. How much interest will she have earned after 10 years?

$155,617.27

Converting & Evaluating

100

Convert the following to log form

3^x = 8

log₃8 = x

200

Convert the following to exponential form

log₆13 = n

6ⁿ = 13

300

Evaluate 

log₃0

undefined

400

Solve

log(3x - 2) = 2

x = 34

500

Evaluate 

log₃(1/243)

-5

Logarithmic Inverses & Graphs

100

What is the asymptote of y = log(x - 5) + 7

x= 5

200

State the transformations of g(x) = -(1/2)lnx+4

reflection over the x-axis

VC of 1/2

up 4

300

Find the inverse of h(x) = log₇(x - 4)

h^-1(x) = 7^x + 4

400

What is the inverse of f(x) = 3^x+2 +17

f^-1(x) = log₃(x - 17) - 2

500

Find the inverse of R = 12log(a + 1) +25

f^-1(R) = 10^(R-25)/12 - 1

Properties of Logarithms

100

Expand log₅ (17x)

log₅17 + log₅x

200

Condense 

log₃x - log₃y

log₃ (x/y) 

300

Expand 

log5²x⁴

2log5 + 4logx

400

Condense 

1/3log₄x + log₄y + 5log₄z

log₄ (x^1/3yz⁵)

500

Condense 

logx - 2logy + 3logz

log (xz³/y²)

Exponential and Logarithmic Equations

100

Solve

2^x=2^2x+7

x = -7

200

Solve

9^x-2 = 27^3x

x= -4/7

300

Solve 

log₆(5x-1)=log₆(2x+8)

x=3

400

Solve

log₂4 + log₂x = 6

x=16

500

Solve

5^x+3=10 

x = -1.57