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mathematics
college algebra
Intermediate Algebra 13th Edition Margaret Lial, John Hornsby, Terry McGinnis - Solutions
In Problems 23–26, write each expression as the sum and/or difference of logarithms. Express powers as factors. (1²) W log3 u> 0, v> 0, w > 0.
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. log (2x) - log(x - 3) = 1
In Problems 15–22, find the principal needed now to get each amount; that is, find the present value.To get $750 after 2 years at 2.5% compounded quarterly.
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. logo (x + 4) + log6(x + 3) = 1
In Problems 21–26, the graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one. -3 у 3 3 x
In Problems 27–29, write each expression as a single logarithm. 3 log4x² + log4 Vx 2
In Problems 13–28, use properties of logarithms to find the exact value of each expression. Do not use a calculator. 5log,6+log57
In Problems 20–22, find the exact value of each expression. Do not use a calculator.2log2 0.4
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. logg (x + 6) = 1 - logg (x + 4)
In Problems 13–28, use properties of logarithms to find the exact value of each expression. Do not use a calculator. elog e29
In Problems 13–28, use properties of logarithms to find the exact value of each expression. Do not use a calculator. elog 2 16
In Problems 23–26, find the effective rate of interest.For 4% compounded continuously.
In Problems 27–29, write each expression as a single logarithm. - 1 X In (¹) + In (₁) In (x² - 1) n(* = x + - - x + 1 1)
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. logo (x + 8) + logg (x + 7) = 2
In Problems 27–32, the graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 . -2 y 2 -2- y = x 2 X
In Problems 17–28, approximate each number using a calculator. Express your answer rounded to three decimal places.125e0.026(7)
In Problems 17–28, approximate each number using a calculator. Express your answer rounded to three decimal places.83.6e-0.157(9.5)
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.In(x + 1) - ln x = 2
In Problems 27–38, find the exact value of each logarithm without using a calculator.log1/5 125
Graph y = log3 x using a graphing utility and the Change-of-Base Formula.
In Problems 27–38, find the exact value of each logarithm without using a calculator.log7 49
The data in the table below represent the U.S. online advertising revenues for the years 2005–2016. (a) Using a graphing utility, draw a scatter plot of the data using 0 for 2005, 1 for 2006, and so on as the independent variable, and online advertising revenue as the dependent variable. (b)
In Problems 8–11, evaluate each expression. without using a calculator. glog₂5
In Problems 8–11, evaluate each expression. without using a calculator.log 10,000
In Problems 7–14, find the amount that results from each investment.$1200 invested at 5% compounded daily after a period of 3 years.
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.log4|x| = 3
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. log₂|x - 7| = 4
In Problems 8–11, evaluate each expression. without using a calculator.ln e7
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.log5 |2x - 1| = log5 13
In Problems 11–14, each function is one-to-one. Find the inverse of each function and check your answer. Find the domain and range of f and f-1. f(x)=√x - 2
Simplify. If 3x = 34, then x = _____∙
Given f(x) = 3x and g(x) = log3 x, evaluate each of the following. (a) f(4) (b) g (9) (c) f(-2) (d) g 1 27
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. 1 -log7 x = 3 log72
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. log, 3x + 4 = log9|5x - 12|
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. 2 log5 x = 3 log5 4
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. 3 log₂x = log2 27
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. 2 log(x - 5) + log69 = 2
In Problems 14–19, solve each equation. Express irrational solutions in exact form. log(x² + 3) = log (x + 6)
In Problems 11–14, each function is one-to-one. Find the inverse of each function and check your answer. Find the domain and range of f and f-1 .f(x) = x1/3 + 1
In Problems 14–19, solve each equation. Express irrational solutions in exact form.5x+2 = 125
In Problems 14–19, solve each equation. Express irrational solutions in exact form.log(x + 9) = 2
In Problems 14–19, solve each equation. Express irrational solutions in exact form.8 - 2e-x = 4
In Problems 15–22, find the principal needed now to get each amount; that is, find the present value.To get $1500 after 2 1/2 years at 1.5% compounded daily.
In Problems 14–19, solve each equation. Express irrational solutions in exact form.7x+3 = ex
Simplify loga Mr =______.
In Problems 7–14, find the amount that results from each investment.$900 invested at 3% compounded semiannually after a period of 2 1/2 years.
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form. log4(x + 4) = log4 15
In Problems 8–11, evaluate each expression. without using a calculator. 1 1086 36
The graph of a function f is given below. State why f is one-to-one. Then draw the graph of the inverse function f-1. -4 У 4 (-1,-3)_4 y=x✔ (3, 3) (2,0) 4 x (0, -2)
The population of a midwestern city is declining according to the exponential law. (a) If N is the population of the city and t is the time in years, express N as a function of t. (b) If the population decreased from 900,000 to 800,000 from 2016 to 2018, what will the population be in
In Problems 5–7, solve each equation.log5 x = 4
The data in the table below represent the percent of U.S. citizens aged 12 and older who have a profile on at least one social network. (a) Using a graphing utility, draw a scatter plot of the data using 8 for 2008, 9 for 2009, and so on, as the independent variable, and percent on social
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.log2 (5x) = 4
In Problems 5–7, solve each equation.logb16 = 2
In Problems 5–44, solve each logarithmic equation. Express irrational solutions in exact form.log (x + 6) = 1
The principal that must be invested now so that it will grow to a given amount in a specified time period is called the __________. (a) Present value (b) Future value (c) Interest (d) Effective rate
Simplify loga 1 =_____.
In Problems 43–58, (a) Find the vertex and the axis of symmetry of each quadratic function, and determine whether the graph is concave up or concave down. (b) Find the y-intercept and the x-intercepts, if any. (c) Use parts (a) and (b) to graph the function. (d) Find the
True or False The y-coordinate of the vertex of f(x) = -x2 + 4x + 5 is f(2).
Translate the following sentence into a mathematical equation: The area A of a circle equals the product of the square of its radius r and the constant π.
In Problems 5–7, solve each equation. 3x = 243
In Problems 1–3, for each pair of functions f and g, find: (a) (fog) (2) (b) (gof) (-2) (c) (ff) (4) (d) (gog) (-1)
The data in the table below represent annual revenue of Tesla, Inc. from 2010 to 2017.(a) Using a graphing utility, draw a scatter plot of the data using 0 for 2010, 1 for 2011, and so on, as the independent variable. (b) Using a graphing utility, build an exponential model from the data. (c)
Simplify loga ar =______.
In Problems 1–3, for each pair of functions f and g, find: (a) (fog)(2) (b) (gof) (-2) (c) (fof) (4) (d) (gog) (-1)
Determine which points are on the graph of x2 + y2 = 1. (a) 22, (b) 1 V3 2' 2
The data in the table below represent the number of dairy farms (in thousands) and the amount of milk produced (in billions of pounds) in the United States for various years. (a) Using a graphing utility, draw a scatter plot of the data with the number of dairy farms as the independent
Simplifyloga (MN) = _____+_____.
Find the indicated term for each geometric sequence. 1 1 1 2'6' 18 ; 912
Perform the indicated operations. (2m³3m² + 8m) - (7m³ +5m - 8)
Find the indicated term for each geometric sequence. 2 1 1 3'3'6 ; 918
Use the binomial theorem to expand each binomial. (m + n) 4
Use the binomial theorem to expand each binomial. (x + r) 5
Perform the indicated operations. (614+ 5t3 18t2 + 14t 1) (3t - 2) 응
Find the number of terms in each arithmetic sequence.7, 10, 13, . . . , 49
Find the indicated term for each geometric sequence. a₂ = 18, a5-486; a
Determine an expression for the general term of each arithmetic sequence. Then find a25.-3, 0, 3,. . .
Find the indicated term for each arithmetic sequence. a₁ = 4, d = 3; 925
Determine an expression for the general term an of each sequence.4, 8, 12, 16, . . .
Find the number of terms in each arithmetic sequence.5, 1, -3, . . . , -79
Use the binomial theorem to expand each binomial. (a - b) 5
Determine an expression for the general term of each arithmetic sequence. Then find a25.-10, -5, 0,. . .
Perform the indicated operations. (8 + 3i)(8 - 3i)
Find the indicated term for each geometric sequence. -384; 910 a5 = 48, ag = -384;
Determine an expression for the general term an of each sequence.7, 14, 21, 28, . . .
Find the indicated term for each arithmetic sequence. a₁ = 1, d= -3; 912
Evaluate S8 for each arithmetic sequence.a1 = -2, d = 6
Determine an expression for the general term an of each sequence.-8, -16, -24, -32,. . .
Evaluate S8 for each arithmetic sequence.an = -2 + 5n
Use the binomial theorem to expand each binomial. (p = q)4
Factor. 62³ +52² - 4z
Use the binomial theorem to expand each binomial. (2x + 3)³
Determine an expression for the general term an of each sequence. 1 1 1 1 3'9'27' 81
Factor. 49a¹ - 9b²
Find the indicated term for each arithmetic sequence. 2, 4, 6, ...; a24
Determine an expression for the general term of each geometric sequence. 22 2 3' 15' 75'
Determine an expression for the general term an of each sequence.-10, -20, -30, -40,. . .
Find the indicated term for each arithmetic sequence. 1, 5, 9, ...; a50
Write the first five terms of each geometric sequence.a1 = 2, r = 3
Use the binomial theorem to expand each binomial. (4x + 2)³
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