25 question Precalculus homework
IT_homework2
precal.docx1.
Use the properties of logarithms to simplify the expression.
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1 |
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6 |
log6 36
Complete the table to determine the balance A for $2200 invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent.)
r = 2%, t = 41 years
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n |
1 |
2 |
4 |
12 |
365 |
Continuous |
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A |
$ |
$ |
$ |
$ |
$ |
$ |
Use the properties of natural logarithms to rewrite the expression.
eln 37
4.–/2 pointsLarPreCalcRMRPAlt6 4.2.010.MI.My Notes |
Write the logarithmic equation in exponential form. For example, the exponential form of log5 25 = 2 is 52 = 25.
log
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1 |
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1,000,000 |
= -6
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= |
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5.–/2 pointsLarPreCalcRMRPAlt6 4.2.032.My Notes |
Solve the equation for x.
log12(12) = x
6.–/2 pointsLarPreCalcRMRPAlt6 4.3.064.My Notes |
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
logb
y3 |
||
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z3 |
7.–/2 pointsLarPreCalcRMRPAlt6 4.3.014.My Notes |
Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places.
log13(8)
8.–/2 pointsLarPreCalcRMRPAlt6 4.4.040.My Notes |
Solve the logarithmic equation.
ln x = −15
x =
9.–/2 pointsLarPreCalcRMRPAlt6 4.2.034.My Notes |
Solve the equation for x.
log3 3−2 = x
x =
10.–/2 pointsLarPreCalcRMRPAlt6 4.1.012.My Notes |
Graph the exponential function by hand. Identify any asymptotes and intercepts and determine whether the graph of the function is increasing or decreasing. (Enter NONE in any unused answer blanks.)
Equation of horizontal asymptote: Equation of vertical asymptote: Value of y-intercept Value of x-intercept The function is .
11.–/2 pointsLarPreCalcRMRPAlt6 4.3.010.My Notes |
Consider the following.
loga
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3 |
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4 |
(a) Rewrite the logarithm as a ratio of common logarithms. (b) Rewrite the logarithm as a ratio of natural logarithms.
12.–/2 pointsLarPreCalcRMRPAlt6 4.4.146.My Notes |
Find the time t required for a $1500 investment to double at interest rate r, compounded continuously, and triple at interest rate r, compounded continuously. Round your results to two decimal places.
r = 2.75%
(a) double at interest rate r, compounded continuously t = yr (b) triple at interest rate r, compounded continuously t = yr
13.–/2 pointsLarPreCalcRMRPAlt6 4.4.102.My Notes |
Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answers using a graphing utility. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
log10 x2 = 8
x =
14.–/2 pointsLarPreCalcRMRPAlt6 4.4.044.My Notes |
Solve the logarithmic equation.
log10(x) = –2/3
x =
15.–/2 pointsLarPreCalcRMRPAlt6 4.3.016.My Notes |
Evaluate the logarithm using the change-of-base formula. Round your result to three decimal places.
log5(0.015)
16.–/2 pointsLarPreCalcRMRPAlt6 4.4.112.MI.My Notes |
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.)
log(4x) – log(4 + √x) = 2
x =
17.–/2 pointsLarPreCalcRMRPAlt6 4.5.014.My Notes |
Complete the table for a savings account in which interest is compounded continuously.
|
Initial Investment |
Annual % Rate |
Time to Double |
Amount After 10 years |
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$2300 |
1.3% |
years |
$ |
|
$1000 |
% |
11 years |
$ |
|
$200 |
% |
years |
$425.51 |
|
$ |
1.7% |
years |
$2400.00 |
18.–/2 pointsLarPreCalcRMRPAlt6 4.4.144.My Notes |
Find the time t required for a $1300 investment to double at interest rate r, compounded continuously, and triple at interest rate r, compounded continuously. Round your results to two decimal places.
r = 6%
(a) double at interest rate r, compounded continuously t = yr (b) triple at interest rate r, compounded continuously t = yr
19.–/2 pointsLarPreCalcRMRPAlt6 4.1.010.My Notes |
Graph the exponential function by hand. Identify any asymptotes and intercepts and determine whether the graph of the function is increasing or decreasing. (Enter NONE in any unused answer blanks.)
Equation of horizontal asymptote: Equation of vertical asymptote: Value of y-intercept Value of x-intercept The function is .
20.–/2 pointsLarPreCalcRMRPAlt6 4.2.036.My Notes |
Solve the equation for x.
log4(43) = x
21.–/2 pointsLarPreCalcRMRPAlt6 4.2.082.My Notes |
Use the properties of natural logarithms to rewrite the expression.
ln(e6)
22.–/2 pointsLarPreCalcRMRPAlt6 4.4.030.My Notes |
Solve the exponential equation.
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6 |
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7 |
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x |
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=
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216 |
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343 |
x =
23.–/2 pointsLarPreCalcRMRPAlt6 4.2.088.My Notes |
Use the properties of natural logarithms to rewrite the expression.
ln
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1 |
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e6 |
24.–/2 pointsLarPreCalcRMRPAlt6 4.4.032.My Notes |
Solve the exponential equation. (Round your answer to three decimal places.)
ex = 64
x =
Condense the expression to the logarithm of a single quantity.
9[ln z + ln(z + 5)] − 3 ln(z − 8)
