Logarithmic Expressions Review Quiz

Authored by Emily Baker

Mathematics

9th Grade

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MULTIPLE SELECT QUESTION

30 sec • 1 pt

Which TWO of the following logarithmic expressions is equal to −4? Circle your answers.

$\log_3\left(\frac{1}{81}\right)$

$\log_381$

$\log_3\left(-12\right)$

log 6 − log 10

log $10^{-4}$

Answer explanation

log3(1/81) = log3(3^-4) = -4 and log(10^-4) = -4. Thus, these two expressions equal -4.

MULTIPLE SELECT QUESTION

30 sec • 1 pt

Which TWO of the following logarithms is undefined? Circle your answers.

$\log_20$

$\log_21$

$\log_2\left(\frac{1}{2}\right)$

$\log_2\left(-16\right)$

$\log_232$

Answer explanation

Logarithms are undefined for non-positive numbers. log2 0 is undefined because you cannot take the log of zero, and log2 (−16) is undefined because the argument is negative. Thus, the correct answers are log2 0 and log2 (−16).

If $\log_{15}b$ is equal to 0, what must be the value of b? Circle your answer.

Answer explanation

If log15 b = 0, it means 15 raised to the power of 0 equals b. Since any number to the power of 0 is 1, b must be 1. Therefore, the correct answer is 1.

Which logarithm below is equal to 1? Circle your answer.

$\log_51$

$\log_50$

$\log_55$

$\log_5\left(\frac{1}{5}\right)$

Answer explanation

The logarithm log5 5 equals 1 because the logarithm of a number to its own base is always 1. The other options do not equal 1: log5 1 equals 0, log5 0 is undefined, and log5 (1/5) is negative.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand log 9n.

log 9 + log n

log 9 * log n

log 9 - log n

log 9 / log n

Answer explanation

Using the properties of logarithms, specifically the product property, we can expand log(9n) as log(9) + log(n). Therefore, the correct choice is log 9 + log n.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand $log 5x^3y$ .

log 5 + 3 log x + log y

log 5 + log 3x + log y

log 5x + 3 log y

log 5 + log 3 + log x + log y

Answer explanation

To expand log 5x^3y, use the properties of logarithms: log(ab) = log a + log b and log(a^b) = b log a. Thus, log 5x^3y = log 5 + log(x^3) + log y = log 5 + 3 log x + log y. The correct choice is log 5 + 3 log x + log y.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand log (c/45).

log(c) - log(45)

log(c) + log(45)

log(c)/log(45)

log(45) - log(c)

Answer explanation

Using the properties of logarithms, specifically the quotient rule, we can expand log(c/45) as log(c) - log(45). Thus, the correct choice is log(c) - log(45).

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand $\log \left( \frac{10x^3}{y^4} \right)$ .

log 10 + 3 log x - 4 log y

log 10 + $log x^3$ - $log y^4$

log $10x^3$ - log $y^4$

log 10 + 3 log x + 4 log y

Answer explanation

To expand \log \left( \frac{10x^3}{y^4} \right), use the properties: \log \left( \frac{a}{b} \right) = \log a - \log b \text{ and } \log a^n = n \log a. This gives \log 10 + 3 \log x - 4 \log y, which matches the correct choice.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand $\log \left(\frac{4x^3}{11y^2}\right)$ .

log(4) + 3log(x) - log(11) - 2log(y)

$log(4) + log(x^3) - log(11) - log(y^2)$

$log(4x^3) - log(11y^2)$

log(4) + log(x) - log(11) - log(y)

Answer explanation

Using the properties of logarithms, we expand \log \left(\frac{4x^3}{11y^2}\right) = \log(4) + \log(x^3) - \log(11) - \log(y^2). Then, applying the power rule gives us \log(4) + 3\log(x) - \log(11) - 2\log(y), which is the correct choice.

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand $log(3x^4y^2)^4$ .

4log(3) + 16log(x) + 8log(y)

log(3) + 4log(x) + 2log(y)

4log(3) + 4log(x) + 2log(y)

log(3) + 16log(x) + 8log(y)

Answer explanation

Using the power rule of logarithms, we expand log(3x^4y^2)^4 as 4 * log(3x^4y^2). Then, applying the product and power rules, we get 4log(3) + 44log(x) + 42log(y), simplifying to 4log(3) + 16log(x) + 8log(y). Thus, the correct choice is 4log(3) + 16log(x) + 8log(y).

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Logarithmic Expressions Review

Which TWO of the following logarithmic expressions is equal to −4? Circle your answers.

log3(1/81) = log3(3^-4) = -4 and log(10^-4) = -4. Thus, these two expressions equal -4.

Which TWO of the following logarithms is undefined? Circle your answers.

Logarithms are undefined for non-positive numbers. log2 0 is undefined because you cannot take the log of zero, and log2 (−16) is undefined because the argument is negative. Thus, the correct answers are log2 0 and log2 (−16).

If log⁡15b\log_{15}blog15​b is equal to 0, what must be the value of b? Circle your answer.

If log15 b = 0, it means 15 raised to the power of 0 equals b. Since any number to the power of 0 is 1, b must be 1. Therefore, the correct answer is 1.

Which logarithm below is equal to 1? Circle your answer.

The logarithm log5 5 equals 1 because the logarithm of a number to its own base is always 1. The other options do not equal 1: log5 1 equals 0, log5 0 is undefined, and log5 (1/5) is negative.

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand log 9n.

Using the properties of logarithms, specifically the product property, we can expand log(9n) as log(9) + log(n). Therefore, the correct choice is log 9 + log n.

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand log5x3ylog 5x^3ylog5x3y .

To expand log 5x^3y, use the properties of logarithms: log(ab) = log a + log b and log(a^b) = b log a. Thus, log 5x^3y = log 5 + log(x^3) + log y = log 5 + 3 log x + log y. The correct choice is log 5 + 3 log x + log y.

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand log (c/45).

Using the properties of logarithms, specifically the quotient rule, we can expand log(c/45) as log(c) - log(45). Thus, the correct choice is log(c) - log(45).

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand log⁡(10x3y4)\log \left( \frac{10x^3}{y^4} \right)log(y410x3​) .

To expand \log \left( \frac{10x^3}{y^4} \right), use the properties: \log \left( \frac{a}{b} \right) = \log a - \log b \text{ and } \log a^n = n \log a. This gives \log 10 + 3 \log x - 4 \log y, which matches the correct choice.

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand log⁡(4x311y2)\log \left(\frac{4x^3}{11y^2}\right)log(11y24x3​) .

Using the properties of logarithms, we expand \log \left(\frac{4x^3}{11y^2}\right) = \log(4) + \log(x^3) - \log(11) - \log(y^2). Then, applying the power rule gives us \log(4) + 3\log(x) - \log(11) - 2\log(y), which is the correct choice.

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand log(3x4y2)4log(3x^4y^2)^4log(3x4y2)4 .

Using the power rule of logarithms, we expand log(3x^4y^2)^4 as 4 * log(3x^4y^2). Then, applying the product and power rules, we get 4log(3) + 4*4log(x) + 4*2log(y), simplifying to 4log(3) + 16log(x) + 8log(y). Thus, the correct choice is 4log(3) + 16log(x) + 8log(y).

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If $\log_{15}b$ is equal to 0, what must be the value of b? Circle your answer.

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand $log 5x^3y$ .

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand $\log \left( \frac{10x^3}{y^4} \right)$ .

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand $\log \left(\frac{4x^3}{11y^2}\right)$ .

Use the properties of logarithms to expand each logarithmic expression. Do NOT leave exponents in your answer. Expand $log(3x^4y^2)^4$ .

Using the power rule of logarithms, we expand log(3x^4y^2)^4 as 4 * log(3x^4y^2). Then, applying the product and power rules, we get 4log(3) + 44log(x) + 42log(y), simplifying to 4log(3) + 16log(x) + 8log(y). Thus, the correct choice is 4log(3) + 16log(x) + 8log(y).