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• Exponents and Logarithms
• Logarithm tests
• Basic logarithms identities

# Basic logarithms identities

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•  Question 1: 1 pts Simplify.$$\log_{b}x+\log_b{y}$$
 $\log_{b}(x-y)$ $\log_{b}(x^{y})$ $\log_{b}(xy)$ $\log_{b}(x+y)$
•  Question 2: 1 pts Simplify.$$\log_{13}6+\log_{13}4$$
•  Question 3: 1 pts Simplify.$$\log_{17}30-\log_{17}6$$
 $\log_{24}17$ $\log_{17}5$ $\log_{17}24$ $\log_{17}36$
•  Question 4: 1 pts Use the power property to simplify the expression $\log_{5}\sqrt[7]{25}.$
 $\dfrac{5}{2}$ $\dfrac{7}{2}$ $\dfrac{2}{7}$ $\dfrac{5}{7}$
•  Question 5: 2 pts Simplify.$$2\log a+3\log b+4\log c$$
 $\log a^{2}+b^{3}c^{4}$ $\log a^{2}b^{3}+c^{4}$ $\log( a^{2}+b^{3}+c^{4})$ $\log a^{2}b^{3}c^{4}$
•  Question 6: 2 pts Simplify. $$2\log a-3\log(a^{2}+b^{2})$$
 $\log \dfrac{1}{(b^{2})^{3}}$ $\log \dfrac{a^{2}}{(a^{6}+b^{6})}$ $\log \dfrac{a^{2}}{(a^{2}+b^{2})^{3}}$ $\log \dfrac{a^{2}}{(3a^{2}+3b^{2})}$
•  Question 7: 2 pts $$\dfrac{1}{3}\log a+\log b=\log\sqrt[3]{ab}$$
•  Question 8: 2 pts Simplify. $$\log_{8}\log_{4}\log_{2}16$$
 $0$ $2$ $4$ Can't be simplified.
•  Question 9: 3 pts Simplify. $$\log_{\frac{1}{9}}\left(\log_{2}\dfrac{1}{2}\cdot\log_{\frac{1}{2}}8\right)$$
 $1$ $\dfrac{1}{2}$ $-1$ $-\dfrac{1}{2}$
•  Question 10: 3 pts Simplify. $$\log x\cdot \log 12$$
•  Question 11: 3 pts Simplify. $$36^{1-\log_{6}3}+25^{-\log_{5}6}$$
 $\dfrac{145}{36}$ $\dfrac{125}{36}$ $\dfrac{105}{36}$ $\dfrac{75}{36}$
•  Question 12: 3 pts Simplify. $\dfrac{2}{3}\log a+3\log b-\dfrac{2}{5}\log c$
 $\log \dfrac{\sqrt[3]{a^{2}}+ b^{3}}{\sqrt[5]{c^{2}}}$ $\log \dfrac{\sqrt[3]{a^{2}}\cdot b^{3}}{\sqrt[5]{c^{2}}}$ $\log \dfrac{\sqrt[3]{a^{2}}}{b^{3}\cdot{\sqrt[5]{c^{2}}}}$ $\log \dfrac{\sqrt[3]{a^{2}}}{b^{3}+{\sqrt[5]{c^{2}}}}$