Chapter 3

Page 1

Evaluate the function at the indicated value of x. Round to three decimals.

f(x)= 0.9^x

x=1.4

f(x)=(2/3)^5x

x=3/10

f(x)=200(1.2)^12x

x=24

Page 2

Evaluate the function at the indicated value of x. Round to three decimals.

h(x)=e^-x

x=3/4

f(x)= 2e^-5x

x=10

f(x)=5000e^0.006x

x=6

Page 3

Use one-to-one property and solve for x.

3^x+1=27

(1/2)^x=32

e^3x+2=e^3

e^(2^x)-3=e^2x

Page 4

Determine the balance A for P dollars invested at rate r for t years and compounded n time per year. - Compound Interest Formula: A=P((1+(r/n))^(nt)

P=$1500, r=2%, t=10 years

P=$2500, r=4%, t= 20 years

Page 5

Determine balance A for $12,000 invested at rate r for t years, compounded continuously. Formula: A=Pe^rt

r=4%

r=6.5%

Page 6

Write the logarithmic equation in exponential form.

log(4)16=2

log(9)1/81=-2

log(32)4=2/5

log(64)8=1/2

Page 7

Write the exponential equation in logarithmic form.

5^3=125

81^(1/4)=3

6^-2= 1/36

24^0=1

Page 8

Evaluate the function at the indicated value of x without using a calculator.

f(x)= log(2)x

x=64

f(x)= log(8)x

x=1

f(x)=log(a)x

x=a^2

Page 9

Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch the graph.

f(x)=log(4)x

y=-log(3)x+2

f(x)=-log(6)(x+2)

y=log(x/7)

Page 10

Write the exponential equation in logarithmic form.

e^4=54.598

e^1/2=1.6487

e^-0.9=0.406

e^x=4

Page 11

Write the logarithmic equation in exponential form.

ln(1/2)=-.0693

ln7=1.945

ln250=5.521

ln1=0

Page 12

Evaluate g(x)=lnx at the indicated value of x without using a calculator

x=e^5

x=e^-5/6

Page 13

Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its graph.

f(x)=ln(x-4)

g(x)= ln(-x)

Page 14

Evaluate the logarithm using the change-of-base formula, round to three decimals.

log(3)7

log(1/2)4

log(9)0.1

log(15)1250

Page 15

Use properties of logarithms to rewrite and simplify the logarithmic expression.

log(4)8

log (5) 1/250

ln(5e^6)

Page 16

Find the exact value without using the calculator.

log(3)9

log(4)16^2

log(2) (-2)

Page 17

Condense the expression to the logarithm of a single quantity.

ln2+lnx

log(4)z-log(4)y

2log(2)x+4log(2)y

1/4log(3)5x

logx-2log(x+1)

logs-2logy+3logz

lnx-[ln(x+1)+ln(x-1)]

1/3[2ln(x+3)+lnx-ln(x^2-1)]

1/3[log(8)y+2log(8)(y+4)]-log(8)(y-1)

Page 18

Solve the exponential equation algebraically.

e^x=e(^x^2)-2

4(3^x)=20

2e^x=10

e^x-9=19

3^2x=80

5^-t/2=0.20

3^x-1=27

2^3-x=565

Page 19