Exponential and Logarithmic Equations Review

Fill in the _____

100

To _______ an equation for x means to find all values of x. 

Solve

200

a^x = a^y, meaning _________.

x = y

300

(a^x)^y = __________.

a^xy

400

1/a^x= 

a^(-x)

500

sqrt(x)

x^(1/2)

Solving Simple Equations

100

Solve for x. 

4^x=16

x = 2

200

Solve for x. 

25^x=1/125

x=-3/2

300

Solve for x. 

(1/4)^x=64

x = -3

400

Solve for x. 

\sqrt(32)=4^x

x = 5

500

Solve for x.

8^x=1/64

x = -2

Exponential Equations

100

Solve. 2^x =4^(x+1)

What is -2?

200

Solve. 4^-3x=4²

What is x=2/3

300

Solve for x. 2^x+2=16

x = 2

400

Solve for x. 4^-3x=64^3-x

x = 14.456525

500

Solve for x. 3^3x+2=7^3x

x = 0.02885715

Creating Formulas

100

Create the formula for the following equation: 

The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams would be left after 7.2 minutes has elapsed?

y=100.0(1/2)^(x/2.4)

200

Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. Write down an exponential decay function for a 90-gram sample.

y=90(1/2)^(x/17.5)

300

Lea invests $8,333 in a savings account with a fixed annual interest rate of 8% compounded 2 times per year.

y=8333(1.04)^(4n)

400

A bacteria colony has an initial population of 200. The population triples every week.

y=200(3)^x

500

An investment of $4000 earns interest, which causes it to increase by 6% per year.

y=4000(1.06)^x

Graphs

100

Is the function increasing and decreasing?

y=3(6/5)^x

Increasing

200

What is the domain of the function?

y=3(6/5)^x

{x|x\in\R}

300

What is the y-intercept of the function?

(0,3)

400

What is the range of the function?

y=3(6/5)^x

{y|y>0,y\in\R}

500

What is the end behaviour of the function?

From QII to QI