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study help
mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
Graph each logarithmic function. g(x) = log1/6 X
Graph each logarithmic function. f(x) = log6 x
Graph each logarithmic function. g(x) = log1/4 x
Graph each logarithmic function. g(x) = log5 x
Graph each logarithmic function. f(x) = log1/3 x
Graph each logarithmic function. g(x) = log3 x
Why is a negative number not allowed as a base for a logarithmic function?
Use the special properties of logarithms to evaluate each expression. log6 V6
Graph each logarithmic function. f(x) = log4 x
Why is 1 not allowed as a base for a logarithmic function?
Use the special properties of logarithms to evaluate each expression. log, V9
Use the special properties of logarithms to evaluate each expression. 1 log6 6
Use the special properties of logarithms to evaluate each expression. log4 1 4
Previously, we solved an equation such as 5x = 125 as follows.Solution set: {3}The method described in this section can also be used to solve this equation. Work Exercises in order, to see how this is done.Use a calculator to find the decimal form of the solution. What is the solution set? 5x 5 =
Use the special properties of logarithms to evaluate each expression.log3 27
Use the special properties of logarithms to evaluate each expression.log3 81
Use the special properties of logarithms to evaluate each expression.5log5 11
Which plan is better? How much more would it pay?Plan A: Invest $1000 at 4% compounded quarterly for 3 yrPlan B: Invest $1000 at 3.9% compounded monthly for 3 yr L OOL
Use the special properties of logarithms to evaluate each expression.log2 128
Use the special properties of logarithms to evaluate each expression.log2 64
Find the half-life of a radioactive substance that decays according to the function Q(t) = A0e-0.05t, where t is in days, to the nearest tenth. L OOL
Use the special properties of logarithms to evaluate each expression.8log8 5
Use the special properties of logarithms to evaluate each expression.12log12 3
Use the special properties of logarithms to evaluate each expression.log4 4-6
Use the special properties of logarithms to evaluate each expression.log2 2-1
Use the special properties of logarithms to evaluate each expression.log5 56
How much will $10,000 compounded continuously at 3.75% annual interest amount to in 3 yr? L OOL
Use the special properties of logarithms to evaluate each expression.log4 49
Use the special properties of logarithms to evaluate each expression.log12 1
Use the special properties of logarithms to evaluate each expression.log5 1
Use the special properties of logarithms to evaluate each expression.log8 8
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.logπ 10
The concentration of a drug in a person’s system decreases according to the functionwhere C(t) is in appropriate units, and t is in hours. Approximate answers to the nearest hundredth.(a) How much of the drug will be in the system after 1 hr?(b) How long will it take for the concentration to be
A sample of 400 g of lead-210 decays to polonium-210 according to the functionwhere t is time in years. Approximate answers to the nearest hundredth.(a) How much lead will be left in the sample after 25 yr?(b) How long will it take the initial sample to decay to half of its original amount? A(t)
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places. 10% V/5 log6
Solve each equation. Give exact solutions. log₂x + log₂ (x + 15) = log₂ 16
Suppose $20,000 is deposited at 4% annual interest compounded quarterly. How much will be in the account at the end of 5 yr? (Assume no withdrawals are made.) L OOL
Use the special properties of logarithms to evaluate each expression.log3 3
Solve each equation. log 1/3 (x4) = 2
A major scientific periodical published an article in 1990 dealing with the problem of global warming. The article was accompanied by a graph that illustrated two possible scenarios.(a) The warming might be modeled by an exponential function of the form(b) The warming might be modeled by a linear
A major scientific periodical published an article in 1990 dealing with the problem of global warming. The article was accompanied by a graph that illustrated two possible scenarios.(a) The warming might be modeled by an exponential function of the form(b) The warming might be modeled by a linear
Suppose that the amount, in grams, of radium-226 present in a given sample is determined by the functionwhere t is measured in years. Approximate the amount present, to the nearest hundredth, in the sample after the given number of years.(a) 20 (b) 100 (c) 500 (d) What was the initial amount
Solve each equation. log 1/2 (2x - 1) = 3
When does the object in Exercise 43 strike the ground?Data from in Exercise 43An object is projected directly upward from the ground. After t seconds its distance in feet above the ground isAfter how many seconds will the object be 128 ft above the ground? s(t) = 144t 16t².
Solve each equation. Give exact solutions. log4x + log4 (8 - x) = 2
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places. log3 V2
Graph. f(x) = log3 x
Suppose that the amount, in grams, of plutonium-241 present in a given sample is determined by the functionwhere t is measured in years. Approximate the amount present, to the nearest hundredth, in the sample after the given number of years.(a) 4 (b) 10 (c) 20 (d) What was the initial amount
Solve each equation. log6 V216 = x
Refer to the function in Exercise 47. Find the time it would take for the car to skid 500 ft.Data from in Exercise 47The following function gives the distance in feet a car going approximately 68 mph will skid in t seconds.Find the time it would take for the car to skid 180 ft. D(t) = 13t² 100t
Solve each inequality, and graph the solution set. x? 3x – 10 2 0
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.logπ e
Graph. f(x) = (x − 1)² + 2 - 1 3
Find the vertex of each parabola. f(x) = 2x² + 4x - 5
Solve each formula for the specified variable. (Leave ± in the answers as needed.) S = 4πr² for r
Solve each equation using the quadratic formula. 2x² + x 210
Solve each equation. Check the solutions. 1 3 X 28 -2 = 0
Solve each equation or inequality. 6+ 15 52 || 19 S
Solve each inequality, and graph the solution set. (x + 4)(x-6)
Solve each equation or inequality. 2x = 5x+2 3
Identify the vertex of each parabola. f(x) || 1 2
The formula A = P(1 + r)2 gives the amount A in dollars that P dollars will grow to in 2 yr at interest rate r (where r is given as a decimal), using compound interest. What interest rate will cause $2000 to grow to $2142.45 in 2 yr?
Solve each formula for the specified variable. (Leave ± in the answers as needed.) S = 6e² for e
Solve each equation. Check the solutions. -12 X = x + 8
Find the vertex of each parabola. f(x) = x² + 10x + 23
Solve each inequality, and graph the solution set. (x + 6) (x - 2) > 0
Solve each equation or inequality. |6x9|=|-4x + 2|
Use the quadratic formula to solve each equation. 4x2 + 12x + 9 = 0
Solve each quadratic equation by the method of your choice.n2 + 6n + 4 = 0
What is the discriminant for 2x2 - 8x - 3 = 0? How many and what type of solutions does this equation have?
The High Roller observation wheel in Las Vegas has a height of about 168 m. Use the metric version of Galileo’s formula, d = 4.9t2 (where d is in meters), to find how long it would take a wallet dropped from the top of the High Roller to reach the ground.
The trinomial 6x2 + 7x - 20 may be factored using substitution.Factor the numerator of the expression from Exercise 78 in terms of the variable t.Data from in Exercise 78The first term in the numerator of the answer from Exercise 77 is now a perfect square. Let t = 6x (the square root of 36x2), and
Solve each equation for the specified variable. 4s + 7p = tp - 7 for p
Inverse functions can be used to send and receive coded information. A simple example might use the functionSuppose that each letter of the alphabet is assigned a numerical value according to its position, as follows.Using the function, the word ALGEBRA would be encoded asbecauseand so on. The
Determine whether each statement is true or false. log38+ log3 1 | 00 8 = 0
How long, to the nearest hundredth of a year, would it take $4000 to double at 3.25% compounded continuously?
Use the change-of-base rule (with either common or natural logarithms) to approximate each logarithm to four decimal places.log4 18
A small business estimates that the value V(t) of a copy machine is decreasing according to the exponential functionwhere t is the number of years that have elapsed since the machine was purchased, and V(t) is in dollars.(a) What was the original value of the machine?(b) What is the value of the
Solve each equation. Approximate solutions to three decimal places.2x-1 = 15
Solve each equation.logπ π4 = x
Find the amount of money in an account after 12 yr if $5000 is deposited at 7% annual interest compounded as follows.(a) Annually (b) Semiannually (c) Quarterly(d) Daily (Use n = 365.) (e) Continuously
Identify the vertex of each parabola. f(x) = x² + 4
Solve each equation by any method. 3- 16 X 12 -2 = 0
Solve each quadratic equation by the method of your choice. (x - 3)² = 25
Solve each equation. Check the solutions. 4- 7 r 2 น = 0
Solve each equation or inequality. (x²2x)² = 11(x² - 2x) - 24
Solve each equation or inequality. 3 x 3 C 2 x-2 3 x2 – 5x+6
Use the quadratic formula to solve each equation.16x2 + 40x + 25 = 0
Solve each inequality, and graph the solution set. (x+4)(x-8)
Solve each formula for the specified variable. (Leave ± in the answers as needed.) s = kwd² for d
Solve each equation using the quadratic formula. r2 +5r = 7
Find the vertex of each parabola. f(x) = -3x² + 12x − 8
Identify the vertex of each parabola. f(x)=x²-4
Solve each quadratic equation by the method of your choice. :55 X + 12 -2 -X = 2 || =
Solve each equation by any method. 4x²7x3=0
Solve each equation or inequality. (r 1) (2r + 3) (r + 6)
Solve each equation. Check the solutions. 3- -I ||
Solve each equation or inequality. (r-5) (2r + 3) = 1
Solve each inequality, and graph the solution set. x² - 4x + 30
Solve each formula for the specified variable. (Leave ± in the answers as needed.) I= ks d² for d
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