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Basic logarithms identities

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  • Question 1:
    1 pts
    		Simplify.log⁡bx+log⁡by\log_{b}x+\log_b{y}
    log⁡b(x−y)\log_{b}(x-y)
    log⁡b(xy)\log_{b}(x^{y})
    log⁡b(xy)\log_{b}(xy)
    log⁡b(x+y)\log_{b}(x+y)
  • Question 2:
    1 pts
    		Simplify.log⁡136+log⁡134\log_{13}6+\log_{13}4
  • Question 3:
    1 pts
    		Simplify.log⁡1730−log⁡176\log_{17}30-\log_{17}6

    log⁡2417\log_{24}17

    log⁡175\log_{17}5

    log⁡1724\log_{17}24

    log⁡1736\log_{17}36

  • Question 4:
    1 pts
    		Use the power property to simplify the expression log⁡5257.\log_{5}\sqrt[7]{25}.
    52\dfrac{5}{2}
    72\dfrac{7}{2}
    27\dfrac{2}{7}
    57\dfrac{5}{7}
  • Question 5:
    2 pts
    		Simplify.2log⁡a+3log⁡b+4log⁡c 2\log a+3\log b+4\log c
    log⁡a2+b3c4\log a^{2}+b^{3}c^{4}
    log⁡a2b3+c4\log a^{2}b^{3}+c^{4}
    log⁡(a2+b3+c4)\log( a^{2}+b^{3}+c^{4})
    log⁡a2b3c4\log a^{2}b^{3}c^{4}
  • Question 6:
    2 pts
    		Simplify. 2log⁡a−3log⁡(a2+b2)2\log a-3\log(a^{2}+b^{2})
    log⁡1(b2)3\log \dfrac{1}{(b^{2})^{3}}
    log⁡a2(a6+b6)\log \dfrac{a^{2}}{(a^{6}+b^{6})}
    log⁡a2(a2+b2)3\log \dfrac{a^{2}}{(a^{2}+b^{2})^{3}}
    log⁡a2(3a2+3b2)\log \dfrac{a^{2}}{(3a^{2}+3b^{2})}
  • Question 7:
    2 pts
    		13log⁡a+log⁡b=log⁡ab3\dfrac{1}{3}\log a+\log b=\log\sqrt[3]{ab}
  • Question 8:
    2 pts
    		Simplify. log⁡8log⁡4log⁡216\log_{8}\log_{4}\log_{2}16
    00
    22
    44
    Can't be simplified.
  • Question 9:
    3 pts
    		Simplify. log⁡19(log⁡212⋅log⁡128)\log_{\frac{1}{9}}\left(\log_{2}\dfrac{1}{2}\cdot\log_{\frac{1}{2}}8\right)
    11
    12\dfrac{1}{2}
    −1-1
    −12-\dfrac{1}{2}
  • Question 10:
    3 pts
    		Simplify. log⁡x⋅log⁡12\log x\cdot \log 12
  • Question 11:
    3 pts
    		Simplify. 361−log⁡63+25−log⁡5636^{1-\log_{6}3}+25^{-\log_{5}6}

    14536\dfrac{145}{36}

    12536\dfrac{125}{36}

    10536\dfrac{105}{36}

    7536\dfrac{75}{36}

  • Question 12:
    3 pts
    		Simplify. 23log⁡a+3log⁡b−25log⁡c\dfrac{2}{3}\log a+3\log b-\dfrac{2}{5}\log c
    log⁡a23+b3c25\log \dfrac{\sqrt[3]{a^{2}}+ b^{3}}{\sqrt[5]{c^{2}}}
    log⁡a23⋅b3c25\log \dfrac{\sqrt[3]{a^{2}}\cdot b^{3}}{\sqrt[5]{c^{2}}}
    log⁡a23b3⋅c25\log \dfrac{\sqrt[3]{a^{2}}}{b^{3}\cdot{\sqrt[5]{c^{2}}}}
    log⁡a23b3+c25\log \dfrac{\sqrt[3]{a^{2}}}{b^{3}+{\sqrt[5]{c^{2}}}}

Exponents

Logarithms