200

300

400

500

100

200

300

400

500

100

200

300

400

500

100

200

300

400

500

200

300

400

500

800

100

Graphs & Transfor-mations

Log Properties

SolvingEquations

Solving Equations

Growth & Decay Models

List the transformations in order from f(x) to

g(x)

xxf 5)( =

152)( 3 +×-= +xxg

Left 3Flip over x-axis

Vertical stretch by factor 2Up 1

If f(x) is transformed in the following order, write the resulting equation.

Flip over y-axisHoriz compression by factor ¼ Flip over x-axisVertical compression by factor ¼Down 2

xxf 4log)( =

2)4(log41)( 4 ---= xxg

Make an x, y table for the function. Include four

points.

xxf 2log)( =

x y

½ -11 02 14 2

Determine the domain, range and the vertical

asymptote.

( )1log)( -= xxf

Determine the domain, range, and horizontal

asymptote

2)( += xexf

Evaluate using change of base:

1250log15

2.63

Evaluate

3log75log 55 -

2

Expand & simplify

36

1logx

x6log3-

Expand & simplify

3

2

lnyx

yx ln23ln -

Condense & simplify

3log25log245log 555 -+

3

Solve

3212 2 =-x

3-=x

Solve

( ) 8ln2ln 2 =- xx

24-=

=xx

Solve

( ) 112log5 =-x

49.160»x

Solve

( ) ( ) 25log1log 33 =--+ xx

75.5=x

Solve

2140471.24

9

=÷øö

çèæ -

t

25.0»x

Solve

2433 112 =-x

8=x

Solve

914 =xe

12.3»x

Solve

10ln62 =- x

26.0»x

Solve

0652 =+- xx ee

10.169.0

»»xx

Solvet03.0

26878.0163090 ÷

øö

çèæ -=

22.13»x

Earl invests $10,000 at 6.5% for 30 years. How much

more would Earl earn with interest compounded

continuously rather than monthly?

$368.90

Mortimer invests $1500 at 10.5% interest compounded

monthly. How long does Mortimer have to wait for his investment to triple?

10.51 years

Norma’s investment turned into $500,000

after 40 years at a rate of 12% compounded

continuously. How much did Norma invest?

$4114.87

Gertrude and her great-granddaughters are testing a substance that has a half-life of 4202 years. If she has 3g,

what amount will be left after 150 years?

2.93 grams

Eustace made an investment of $10,000 that

took 12 years to double with interest compounded monthly. What is his

interest rate? How much will Eustace have after a

total of 20 years?

5.79%$31,748.02