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Chapter 5: Q. 9 (page 315)

Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

log4x+2=log48

Short Answer

Expert verified

The solution of the equation is{6}.

Step by step solution

01

Step 1. Given information

Thegivenequationislog4x+2=log48.

We have to express irrational solutions in exact form and as a decimal rounded to three decimal places.

Also, we have to verify the result using the graphing utility.

02

Step 2. Simplify.

Now,Weknow,鈬�logab=logbloga.Thus,鈬�log4x+2=log48鈬�logx+2log4=log8log4鈬�logx+2=log8鈬�x+2=8鈬�x=8鈭�2鈬�x=6

03

Step 3. Verifying the result

Plot the graph of the equation log4x+2=log48using the graphing utility.

From the above graph. we can observe that the graph of the given equation intersects the x-axis atx=6

Therefore, the solution is verified.

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Most popular questions from this chapter

Economics and Marketing The following data represent the price and quantity supplied in 2009 for Dell personal computers.

(a) Using a graphing utility, draw a scatter diagram of the data with price as the dependent variable.

(b) Using a graphing utility, build a logarithmic model from the data.

(c) Using a graphing utility, draw the logarithmic function found in part (b) on the scatter diagram.

(d) Use the function found in part (b) to predict the number of Dell personal computers that will be supplied if the price is $1650.

The graph of an exponential function is given. Match each graph to one of the following functions.

Evaluate each expression using the graphs of y = f(x) and y = g(x) shown in the figure.

(a) (g o f)(-8)

(b) (fog)(-8)

(c) (g o g)(7)

(d) (g o f)(-5)

Use transformations to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=1-2-x/3

Current in a RL Circuit The equation governing the amount of current I(in amperes) after time t(in seconds) in a simple RL circuit consisting of a resistance R(in ohms), an inductance L(in henrys), and an electromotive force E(in volts) is

I=ER1-e-RLt

If E=12volts, R=10ohms, and L=5henrys, how long does it take to obtain a current of 0.5 ampere? Of 1.0 ampere? Graph the equation.
See all solutions

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