Exponential and Logarithmic Equations Chapter Review
Chapter
Chapter 7
Section
Exponential and Logarithmic Equations Chapter Review
Solutions 27 Videos

Write each as a power of 4.

• 64
0.09mins
Q1a

Write each as a power of 4.

• 4
0.05mins
Q1b

Write each as a power of 4.

• \frac{1}{16}
0.14mins
Q1c

Write each as a power of 2.

• (\sqrt[3]{8})^5
0.18mins
Q1d

Write it as a power of 5.

• 20
0.14mins
Q2a

Write it as a power of 5.

• 0.8
0.18mins
Q2b

Solve the equation.

 \displaystyle 3^{5x} = 27^{x -1} 

0.26mins
Q3a

Solve the equation.

 \displaystyle 8^{2x+1} = 32^{x -3} 

0.36mins
Q3b

A 50-mg sample of cobalt-60 decays to 40 mg after 1.6 min.

a) Determine the half-life of cobalt-60.

b) How long will it take for the sample to decay to 5\% of its initial amount?

2.14mins
Q4

 \displaystyle 3^{x - 2} = 5^x 

1.08mins
Q5a

 \displaystyle 2^{k - 2} = 3^{k + 1} 

1.13mins
Q5b

 \displaystyle 4^{2x } -4^x - 20 = 0 

0.40mins
Q7a

 \displaystyle 2^{x } + 12(2)^{-x} = 7 

0.59mins
Q7b

A computer, originally purchased for \$2000, loses value according to the exponential equation V(t) = 2000(\frac{1}{2})^{\frac{t}{h}}, where V is the value, in dollars, of the computer at any time, t, in years, after purchase and h represents the half-life,in years, of the value of the computer. After 1 year, the computer has a value of approximately \$1516.

a) What is the half—life of the value of the computer?

b) How long will it take for the computer to be worth 10\% of its purchase price?

1.41mins
Q8

Evaluate without a calculator.

 \displaystyle \log_68 + \log_627 

0.23mins
Q9a

Evaluate without a calculator.

 \displaystyle \log_4128 - \log_48 

0.22mins
Q9b

Write as a single logarithm.

 \displaystyle \log_78 + \log_74 - \log_716 

0.18mins
Q10a

Write as a single logarithm.

 \displaystyle 2\log a + \log(3b) - \frac{1}{2}\log c 

0.37mins
Q10b

Write as a sum or difference of logarithms. Simplify, if possible.

 \displaystyle \log(a^2bc) 

0.21mins
Q11a

Write as a sum or difference of logarithms. Simplify, if possible.

 \displaystyle \log(\frac{k}{\sqrt{m}}) 

0.26mins
Q11b

Simplify and state any restrictions on the variables.

 \displaystyle \log(2m + 6) -\log(m^2 - 9) 

1.22mins
Q12a

Simplify and state any restrictions on the variables.

 \displaystyle \log(x^2 + 2x - 15) -\log(x^2 - 7x + 12) 

1.28mins
Q12b

Solve.

 \displaystyle \log(2x +10) = 2 

0.14mins
Q13a

Solve.

 \displaystyle 1 - \log(2x) = 0 

0.13mins
Q13b

Solve  \displaystyle \log_2x + \log_2(x + 2) = 3 . Check for extraneous roots.

0.38mins
Q14

When you drink a cup of coffee or a glass of cola, or when you eat a chocolate bar, the percent, P, of caffeine remaining in your bloodstream is related to the elapsed time, t, in hours, by t= 5(\frac{\log P}{\log 0.5}).

a) How long will it take for the amount of caffeine to drop to 20\% of the amount consumed?

b) Suppose you drink a cup of coffee at 9:00 am What percent of the caffeine will remain in your body at noon?

1.25mins
Q16

A savings bond offers interest at a rate of 6.6\%, compounded semi-annually. Suppose that a \\$500 bond is purchased.

a) Write an equation for the value of the investment as a function of time, in years.

b) Determine the value of the investment after 5 years.

c) How long will it take for the investment to double in value?