Q: A deposit of $$5000 is made in a savings account with interest compounded monthly. The balance will triple in 10 years. What is the interest rate for this account? (Use A = P(1$$ + $$r/n)^{nt}$)

$$\dfrac{\ln{3}}{12 \times 10}$$

Question 1

Which of the following is the correct exponential form for $$\log_{3}{27} = x$$?

Accepted Answer

$$3^x = 27$$

Question 2

Rewrite $$\ln{1024} = 11 in $$exponential form.

Accepted Answer

$$e^{11} = 1024$

Question 3

Evaluate $$\log_{5}{25}$$ without a calculator.

Accepted Answer

$$2$$

Question 4

Which of the following is equivalent to $$\log_{2}{8}$$?

Accepted Answer

$$3$$

Question 5

Evaluate $$\log_{4}{16}$$ without a calculator.

Accepted Answer

$$2$$

Question 6

Simplify $$\log_{5}{5} + \log_{5}{2}.$$

Accepted Answer

$$\log_{5}{10}$$

Question 7

Expand $$\ln{(4x^2$)}$$ using logarithm properties.

Accepted Answer

$$\ln{4} + 2\ln{x}$$

Question 8

Combine $$\log_{a}{x} + \log_{a}{y}$$ into a single logarithm.

Accepted Answer

$$\log_{a}{(xy)}$$

Question 9

Evaluate $$\log_{2}{32}$$ without a calculator.

Accepted Answer

$$5$$

Question 10

If $$\log_{b}{x} = 4$$ and $$\log_{b}{y} = 2$$, what is $$\log_{b}{(x/y)}$$?

Accepted Answer

$$2$$

Question 11

Expand $$\ln{\left(\dfrac{4x^2$}{y}\right)}$$ using logarithm properties.

Accepted Answer

$$\ln{4} + 2\ln{x} - \ln{y}$$

Question 12

Combine $$2\log_{3}{x} + \log_{3}{y}$$ into a single logarithm.

Accepted Answer

$$\log_{3}{(x^2$y)}$$

Question 13

Evaluate $$\log_{10}{(1/100)}$$ without a calculator.

Accepted Answer

$$-2$$

Question 14

If $$\log_{2}{x} = 3$$, what is the value of $$x$$?

Accepted Answer

$$8$$

Question 15

A deposit of $$5000 is made in a savings account with interest compounded monthly. The balance will triple in 10 years. What is the interest rate for this account? (Use A = P(1$$ + $$r/n)^{nt}$)

Accepted Answer

$$\dfrac{\ln{3}}{12 	imes 10}$$

Question 16

A radioactive element has a half-life of 125 years. If 125 grams are present now, how much was present 500 years ago? (Use $$A = A_0$ e$$^{kt}$$)

Accepted Answer

$$2000$$ grams

Question 17

A thermometer reading $$100^\circF is $$taken outside where the temperature is $$40^\circF. $$The thermometer reads $$80^\circF $$after 5 minutes. Using Newton's Law of Cooling, how long before the thermometer reads $$50^\circF$$? (Use $$T(t) = T_s + (T_0$ - T_s)e$$^{kt}$$)

Accepted Answer

$$10.5$$ minutes

Question 18

Evaluate $$\log_{2}{(1/8)}$$ without a calculator.

Accepted Answer

$$-3$$

Question 19

If $$\log_{a}{b} = x$$ and $$\log_{a}{c} = y$$, what is $$\log_{a}{(b^2$c^3$$)}$?

Accepted Answer

$$2x + 3y$$

Exponential and Logarithmic Functions: Precalculus Chapter 4 Review Study Notes

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