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• Exponents and Logarithms
• Logarithm tests
• Logarithmic properties

# Logarithmic properties

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•  Question 1: 1 pts $$a^{\log_{a}x}=x$$
•  Question 2: 1 pts $$\log_{a}b=\dfrac{\log_{c}b}{\log_{c}a}$$
•  Question 3: 1 pts Simplify. $$\log_{a^{s}}x$$
 $s\log_{a}x$ $\dfrac{1}{s}\log_{a}x$ $\log_{a}x^{s}$ none of these
•  Question 4: 1 pts Find the correct property for $\log_{a}b.$
 $-\dfrac{1}{\log_{b}a}$ $\dfrac{1}{\log_{b}a}$ $-\log_{b}a$ $\dfrac{1}{\log ab}$
•  Question 5: 2 pts Simplify. $$\log_{10}(\log_{4}(\log_{3}81))$$
 $3$ $4$ $1$ $0$
•  Question 6: 2 pts Evaluate. $$\dfrac{\log_{2}36}{\log_{2}6}$$
 $1$ $2$ $4$ $6$
•  Question 7: 2 pts Evaluate. $$\log_{3}5\cdot \log_{4}9\cdot \log_{5}2$$
•  Question 8: 2 pts Find $x$ from equation $\log_{3}x=3\log_{3}a+2\log_{3}c.$
 $x=a^{3}c^{3}$ $x=a^{2}c^{2}$ $x=ac^{3}$ $x=a^{3}c^{2}$
•  Question 9: 3 pts If $\log 5=a$ and $\log 3=b$ evaluate $\log_{30}8$.
$\log_{30}8=$
•  Question 10: 3 pts Simplify. $$\log_{3}2\cdot\log_{4}3\cdot\log_{5}4\cdot\log_{6}5\cdot\log_{7}6\cdot\log_{8}7$$
 $\dfrac{2}{3}$ $\dfrac{1}{3}$ $\dfrac{1}{4}$ $\dfrac{2}{5}$
•  Question 11: 3 pts If $\log_{14}7=a$ and $\log_{14}5=b$ then
$\log_{35}20 =$
•  Question 12: 3 pts $$\log_{3}7=\log_{\frac{1}{3}}{\dfrac{1}{7}}$$