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Question 1 of 5: Expand each logarithm:
Assume all variables represent positive real numbers.$$\text{log}_{4}\left(\frac{x^3}{y}\right)^3$$
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A
$$\text{log}_{4}(x) + \text{log}_{4}(y)$$
B
$$3\text{log}_{4}(x) + 3\text{log}_{4}(y)$$
C
$$9\text{log}_{3}(x) + 9\text{log}_{4}(y)$$
D
$$9\text{log}_{4}(x) - 3\text{log}_{4}(y)$$
E
$$3\text{log}_{4}(x) + 9\text{log}_{4}(y)$$
Question 2 of 5: Expand each logarithm:
Assume all variables represent positive real numbers.$$\text{log}_{8}(w^5 \sqrt{u})$$
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A
$$\text{log}_{8}(w) + \frac{\text{log}_{8}(u)}{2}$$
B
$$\text{log}_{8}(u) + \frac{\text{log}_{8}(w)}{2}$$
C
$$5\text{log}_{8}(w) + \frac{\text{log}_{8}(u)}{2}$$
D
$$\text{log}_{8}(u) + 5\text{log}_{8}(w)$$
E
$$5\text{log}_{8}(u) + 5\text{log}_{8}(w)$$
Question 3 of 5: Condense each logarithm:
Assume all variables represent positive real numbers.$$4\text{log}_{2}(x) - 24\text{log}_{2}(y)$$
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A
$$\text{log}_{2}\left(\frac{x^4}{y^{24}}\right)$$
B
$$\text{log}_{4}\left(\frac{x^2}{y^{24}}\right)$$
C
$$\text{log}_{2}\left(\frac{24x}{y}\right)$$
D
$$\text{log}_{2}\left(2z\sqrt{x^{6}y}\right)$$
E
$$\text{log}_{24}\left(z\sqrt{xy}\right)$$
Question 4 of 5: Condense each logarithm:
Assume all variables represent positive real numbers.$$3\text{log}_{6}(u) - 15\text{log}_{6}(v)$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\text{log}_{6}\left(w^5 \sqrt[3]{u}\right)$$
B
$$\text{log}_{3}\left(w \sqrt[3]{vu}\right)$$
C
$$\text{log}_{6}\left(\frac{u^3}{v^{15}}\right)$$
D
$$\text{log}_{3}\left(\frac{u^5}{v^3}\right)$$
E
$$15\text{log}_{6}\left(3\sqrt{uv}\right)$$
Question 5 of 5: Condense each logarithm:
Assume all variables represent positive real numbers.$$\text{log}_{7}(c) + \frac{\text{log}_{7}(a)}{2}+ \frac{\text{log}_{7}(b)}{2}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\text{log}_{7}\left(\frac{a^8}{b^4}\right)$$
B
$$\text{log}_{7}\left(\sqrt{abc}\right)$$
C
$$\text{log}_{7}\left(\frac{a^2}{b^8}\right)$$
D
$$\text{log}_{7}\left(2 \sqrt{abc}\right)$$
E
$$\text{log}_{7}\left(c \sqrt{ab}\right)$$

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