A)
B)
C)
D)
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic expressions.
188)
1
2log3 x +log3 y
188)
A)
B)
C)
log3
x
y
D)
Solve the logarithmic equation. Give an exact answer.
189)
log59–log5 x =3
189)
A)
B)
C)
125
9
D)
Solve.
190)
The function A =A0e–0.0099x models the amount in pounds of a particular radioactive material
stored in a concrete vault, where x is the number of years since the material was put into the vault.
If 700 pounds of the material are placed in the vault, how much time will need to pass for only 427
pounds to remain?
190)
A)
B)
C)
55 yr
D)
Evaluate the expression without using a calculator.
191)
log3
1
9
191)
A)
B)
C)
–2
D)
Solve the problem.
192)
The function D(h) =7e–0.4h can be used to determine the milligrams D of a certain drug in a
patient’s bloodstream h hours after the drug has been given. How many milligrams will be present
after 9 hours? Round the answer to two decimal places.
192)
A)
B)
C)
0.19 mg
D)
Determine if the graph represents a function that has an inverse function.
193)
193)
A)
does not have an inverse
B)
has an inverse
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic expressions.
194)
ln x +8 ln y
194)
A)
B)
C)
ln(x +8y)
D)
Solve.
195)
The value of a particular investment follows a pattern of exponential growth. You invested money
in a money market account. The value of your investment t years after your initial investment is
given by the exponential growth model A =5000e0.049t. How much did you initially invest in the
account?
195)
A)
B)
C)
$2500.00
D)
196)
The formula S = A (1 + r)t + 1 – 1
r models the value of a retirement account, where A = the number
of dollars added to the retirement account each year, r = the annual interest rate, and S = the value
of the retirement account after t years. If the interest rate is 5%, how much will the account be
worth after 45 years if $2400 is added each year? Round to the nearest whole number.
196)
A)
B)
C)
$22,622
D)
Solve the equation by expressing each side as a power of the same base and then equating exponents.
197)
4–x=1
16
197)
A)
B)
C)
{2}
D)
Solve.
198)
An endangered species of fish has a population that is decreasing exponentially (A =A0ekt). The
population 10 years ago was 1500. Today, only 800 of the fish are alive. Once the population drops
below 100, the situation will be irreversible. When will this happen, according to the model? Round
to the nearest year.
198)
A)
B)
C)
35 yr
D)
199)
The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and
has a pH of 7. The pH of a solution is given by pH = – log x where x represents the concentration of
the hydrogen ions in the solution in moles per liter. Find the pH if the hydrogen ion concentration
is 1 × 10–6.
199)
A)
B)
C)
–6
D)
Find the composition.
200)
If f(x) =6x2+5x and g(x) =3x, find (f
g)(x).
200)
A)
B)
C)
6x2+8
D)
Find the inverse of the one–to–one function.
201)
f(x) = – 6x
201)
A)
B)
C)
f–1(x) =6x
D)
Solve the equation.
202)
1750e0.75x=8750
202)
A)
B)
C)
8750
0.75 ln 1750
D)
Solve the equation by expressing each side as a power of the same base and then equating exponents.
203)
5x=25
203)
A)
B)
C)
{1}
D)
204)
5–x=125
204)
A)
B)
C)
1
25
D)
Evaluate the expression without using a calculator.
205)
log 0.001
205)
A)
B)
C)
–3
D)
Solve the equation.
206)
2 ln(6x) =16
206)
A)
B)
C)
{e4/3}
D)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
207)
logb(yz6)
207)
A)
logb y +logb(6z)
B)
logb y +6logb z
C)
6logb y +6logb z
D)
6logb(yz)
Solve.
208)
A fossilized leaf contains 5% of its normal amount of carbon 14. How old is the fossil? Use 5600
years as the half–life of carbon 14 and round to the nearest year.
208)
A)
B)
C)
36,725 yr
D)
Solve the logarithmic equation. Give an exact answer.
209)
log8 x +log8(x –63) = 2
209)
A)
B)
C)
{64}
D)
66
Solve the problem.
210)
The formula A =138e0.022t models the population of a particular city, in thousands, t years after
2011. When will the population of the city reach 168 thousand?
210)
A)
B)
C)
2021
D)
Provide an appropriate response.
211)
Use A = P 1 +r
n
nt and A = Pert to solve this problem.
Suppose that you have $2000 to invest. Which investment yields the greater return over 10 years:
6.25% compounded continuously or 6.3% compounded semiannually?
211)
A)
$2000 invested at 6.3% compounded semiannually over 10 years yields the greater return.
B)
$2000 invested at 6.25% compounded continuously over 10 years yields the greater return.
C)
Both investment plans yield the same return.
B
Find the composition.
212)
If f(x) =x + 5 and g(x) = 8x – 9, find (f
g)(x).
212)
A)
B)
C)
8x – 4
D)
A
Solve the problem.
213)
Find out how long it takes a $3100 investment to double if it is invested at 7% compounded
semiannually. Round to the nearest tenth of a year. Use the formula A = P 1 +r
n
nt.
213)
A)
B)
C)
10.3 yr
D)
B
A
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic expressions.
214)
ln 6–2 ln x
214)
A)
B)
C)
ln 6
ln x2
D)
Evaluate the expression without using a calculator.
215)
log 1
10,000
215)
A)
B)
C)
1
10,000
D)
Write the equation in its equivalent exponential form.
216)
3=log2x
216)
A)
B)
C)
2x=3
D)
Find the composition.
217)
If f(x) =x – 6
9 and g(x) =9x + 6, find (g
f)(x).
217)
A)
B)
C)
x + 12
D)
Solve.
218)
The function f(x) =300(0.5)x/100 models the amount in pounds of a particular radioactive material
stored in a concrete vault, where x is the number of years since the material was put into the vault.
Find the amount of radioactive material in the vault after 180 years. Round to the nearest whole
number.
218)
A)
B)
C)
270 pounds
D)
Provide an appropriate response.
219)
Write in exponential form: log416 =2
219)
A)
B)
C)
416 =2
D)
Graph the function by making a table of coordinates.
220)
f(x) =3x
220)
A)
B)
69
C)
D)
Evaluate the expression without using a calculator.
221)
ln 7e
221)
A)
B)
C)
7e
D)
Use the graph of the function to draw the graph of the inverse function.
222)
222)
A)
B)
Solve the problem.
223)
The growth in the mouse population at a certain county dump can be modeled by the exponential
function A(t)=962e0.029t, where t is the number of months since the population was first recorded.
Estimate the population after 33 months.
223)
A)
B)
C)
1253 mice
D)
Simplify the expression.
224)
ln e7y
224)
A)
B)
C)
ln(7y)
D)