Textbook

Advanced Functions McGraw-Hill
Chapter

Chapter 7
Section

Exponential and Logarithmic Equations Chapter Review

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Lectures
2 Videos

Finding the term of investment using logs

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2.08mins

Finding the term of investment using logs

Finding the better investment between two rates

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1.14mins

Finding the better investment between two rates

Solutions
27 Videos

Write each as a power of 4.

`64`

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0.09mins

Q1a

Write each as a power of 4.

`4`

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0.05mins

Q1b

Write each as a power of 4.

`\frac{1}{16}`

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0.14mins

Q1c

Write each as a power of 2.

`(\sqrt[3]{8})^5`

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0.18mins

Q1d

Write it as a power of 5.

- 20

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0.14mins

Q2a

Write it as a power of 5.

- 0.8

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0.18mins

Q2b

Solve the equation.

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

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0.26mins

Q3a

Solve the equation.

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

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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?

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2.14mins

Q4

Solve and leave your answer in exact form.

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

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1.08mins

Q5a

Solve and leave your answer in exact form.

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

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1.13mins

Q5b

Solve and leave your answer in exact form.

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

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0.40mins

Q7a

Solve and leave your answer in exact form.

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

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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 halfâ€”life of the value of the
computer?

**b)** How long will it take for the computer to be worth `10\%`

of its purchase price?

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1.41mins

Q8

Evaluate without a calculator.

```
\displaystyle
\log_68 + \log_627
```

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0.23mins

Q9a

Evaluate without a calculator.

```
\displaystyle
\log_4128 - \log_48
```

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0.22mins

Q9b

Write as a single logarithm.

```
\displaystyle
\log_78 + \log_74 - \log_716
```

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0.18mins

Q10a

Write as a single logarithm.

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

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0.37mins

Q10b

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

```
\displaystyle
\log(a^2bc)
```

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0.21mins

Q11a

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

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

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0.26mins

Q11b

Simplify and state any restrictions on the variables.

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

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1.22mins

Q12a

Simplify and state any restrictions on the variables.

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

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1.28mins

Q12b

Solve.

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

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Q13a

Solve.

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

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0.13mins

Q13b

Solve ```
\displaystyle
\log_2x + \log_2(x + 2) = 3
```

. Check for extraneous roots.

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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?

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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?

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3.09mins

Q17