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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
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