MyMathLab answers

In solving the exponential equation 4^x=7^(x-1), which of the following is not true? a. If xln 4/7=-ln 7, then x=-0.2005. b. If xln 4-xln 7=-ln 7, then x=(-ln 7)/(ln 4/7). c. If 4^x=7^(x-1), then xln 4=(x-1)ln 7. d. If xln 4=(x-1)ln 7, then xln 4-xln 7=-ln7.

a. If xln 4/7=-ln 7, then x=-0.2005.

If an exponential equation can be written in the form b^u=b^v, then which of the following methods may be used to solve the equation? a. Relating the bases by setting u=v. b. Bringing down the exponent on each side. c. Dividing both sides by b. d. Subtracting b^v from both sides.

a. Relating the bases by setting u=v.

Which of the following is true? a. ln e^8=8 b. log5 (2x^3)=3log5 (2x) c. ln 6x^2=2ln 6x d. (log4 x)^2=2log4 x

a. ln e^8=8

If a and b are positive real numbers such that a≠1, b≠1, and u is any positive real number then the logarithmic expression logb u is equivalent to which of the following? a. loga u/loga b b. logu a/logu b c. logu b/logu a d. loga b/loga u

a. loga u/loga b

In solving the logarithmic equation of the form logb (x+a) +logb (x+c)=d, why is it essential to check the solution(s) to the resulting quadratic equation for potential extraneous solutions to the original logarithmic equation? a. Equations of this form can never have more than one solution. b. All solutions must satisfy x+a>0 and x+c>0. c. Any solution must be included in either the interval x≤-c or x≤-a. d. Negative numbers cannot be solutions to logarithmic equations.

b. All solutions must satisfy x+a>0 and x+c>0.

In solving an exponential equation, which of the following is not a sound technique to use? a. First, try writing the exponential equation in the form b^u=b^v and then u=v. b. If the exponential equation has the form ab^x=c, first "take the log of both sides" and then "bring down any exponents". c. If the exponential equation cannot be written in the form b^u=b^v, "take the log of both sides" and then "bring down any exponents". d. If the exponential equation has the form ab^x=c, first divide both sides by the constant a.

b. If the exponential equation has the form ab^x=c, first "take the log of both sides" and then "bring down any exponents".

Which of the following statements is not true for the graph of f(x)=e^x? a. The graph of f(x)=e^x approaches 0 as x approaches negative infinity. b. The graph of f(x)=e^x lies between the graphs of y=3^x and y=4^x. c. The line y=0 is a horizontal asymptote. d. The graph of f(x)=e^x intersects the y-axis at (0,1).

b. The graph of f(x)=e^x lies between the graphs of y=3^x and y=4^x.

The domain of f(x)=logb[g(x)] can be determined by finding the solution to which inequality? a. g(x)≥0 b. g(x)>0 c. g(x)<0 d. g(x)≤0

b. g(x)>0

Which of the following is not true? a. ln 5x-ln 1=ln 5x b. ln x+ln 2x=ln 3x c. 1/2 log(x-1)-3log z+log (5 square root (x-1))/z^3 d. ln (x-1)/(x^2+4) =ln (x-1)-ln (x^2+4)

b. ln x+ln 2x=ln 3x

If b>0, b≠1, u and v represent positive numbers, and r is any real number, which of the following statements is not a property of logarithms? a. logb u/v=logb u-logb v b. logb(u+v)=logb u+logb v c. logb u^r=rlogb u d. logb 1=0

b. logb(u+v)=logb u+logb v

For x>0, b>0 and b≠1, if y=logb x, then which of the following is true? a. y=x^b b. x=b^y c. y=b^x d. x=y^b

b. x=b^y

Which of the following numbers is best approximation of the number e to 4 decimal places? a. 3.1415 b. 7.1461 c. 2.7183 d. 1.6278

c. 2.7183

Which of the following statements is true? a. All boundary points of a rational inequality that are found by determining the values for which the numerator is equal to zero should always be represented by plotting an open circle on a number line. b. All boundary points of a rational inequality should always be represented by plotting a closed circle on a number line. c. All boundary points of a rational inequality that are found by determining the values for which the denominator is equal to zero should always be represented by plotting an open circle on a number line. d. All boundary points of a rational inequality should always be represented by plotting an open circle on a number line.

c. All boundary points of a rational inequality that are found by determining the values for which the denominator is equal to zero should always be represented by plotting an open circle on a number line.

In solving the equation ln (x-1)=2, what is the first step? a. Take the log of both sides. b. Substitute e for ln x. c. Rewrite as an exponential equation. d. Add the constant to both sides.

c. Rewrite as an exponential equation.

Which of the following statements is not true for the graph f(x)=b^x, where 0<b<1? a. The line y=0 is a horizontal asymptote. b. The graph intersects the y-axis at (0,1). c. The graph of f(x)=b^x approaches 0 as x approaches negative infinity. d. The graph of f(x)=b^x approaches 0 as x approaches infinity.

c. The graph of f(x)=b^x approaches 0 as x approaches negative infinity.

To what is the expression logb b^x, for b>0 and b≠1, equal? a. 1 b. e c. x d. b

c. x

Why is the logarithmic property of equality, which says that "if logb u=logb v, then u=v" true? a. It is true because the logarithmic function always intersects the x-axis at the point (1,0). b. It is true because the logarithmic function is an increasing function. c. It is true because the logarithmic function has a vertical asymptote. d. It is true because the logarithmic function is one-to-one.

d. It is true because the logarithmic function is one-to-one.

In the definition of the exponential function f(x)=b^x, what are the stipulations(s) for the base b? a. The base b cannot be a fraction. b. The base b must be greater than or equal to zero. c. The base b must be greater than one. d. The base b must be greater than zero but not equal to 1.

d. The base b must be greater than zero but not equal to 1.

Which of the following statements is not true for the graph of y=logb x for b>1? a. The graph of y=logb x contains the point (1,0). b. The graph of y=logb x contains the point (b,1). c. The line x=0 is a vertical asymptote. d. The graph of y=logb x is decreasing on the interval (0,∞).

d. The graph of y=logb x is decreasing on the interval (0,∞).

Which of the following statements is true for the graph of f(x)=-e^x +2? a. The x-axis is a horizontal asymptote. b. The y-axis is a vertical asymptote. c. The line x=2 is a vertical asymptote. d. The line y=2 is a horizontal asymptote.

d. The line y=2 is a horizontal asymptote.

Which of the following statements about the number e is not true? a. The number e is an irrational number. b. The number e is defined as the value of the expression (1+1/n)^n as n approaches infinity. c. The number e is called the natural base. d. The number e is a rational number.

d. The number e is a rational number.

Which of the following is not true about the expression log7 49? a. This expression is called a logarithms expression. b. This expression represents the power that 7 can be raised to in order to get 49. c. This expression represents the number 2. d. This expression represents the number 7.

d. This expression represents the number 7.

Logarithms are studied for which of the following reasons? a. To be able to solve complex logarithmic equations. b. To validate the logarithmic properties. c. To make student's lives miserable. d. To help in solving exponential equations when relating the bases cannot be used.

d. To help in solving exponential equations when relating the bases cannot be used.

In the equation 60=25 e^0.015t, what is the first step in solving for​ t?

divide both sides by 25

In an exponential decay problem involving​ half-life, what does this term​ mean?

the time it takes for a given quantity to decay to half its original mass

In the exponential growth model P(t)= P_0 e^kt, what does the variable Upper P_0 represent?

the variable P_0 represents the initial amount