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  • 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. $\dfrac{2}{3}\log a+3\log b-\dfrac{2}{5}\log c$
    $\log \dfrac{\sqrt[3]{a^{2}}+ b^{3}}{\sqrt[5]{c^{2}}}$
    $\log \dfrac{\sqrt[3]{a^{2}}\cdot b^{3}}{\sqrt[5]{c^{2}}}$
    $\log \dfrac{\sqrt[3]{a^{2}}}{b^{3}\cdot{\sqrt[5]{c^{2}}}}$
    $\log \dfrac{\sqrt[3]{a^{2}}}{b^{3}+{\sqrt[5]{c^{2}}}}$

Exponents

Logarithms