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Math Help - Someone please help me with the answers to these qeustions logarithms factorising!!!

  1. #1
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    Exclamation Someone please help me with the answers to these qeustions logarithms factorising!!!

    here are the qeustions on this picture, please help me please!! Logaritmhs and factorisingSomeone please help me with the answers to these qeustions logarithms factorising!!!-maths-2-.jpg
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  2. #2
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    Re: Someone please help me with the answers to these qeustions logarithms factorising

    Hello, Jordannn1994!

    2\;\text{Simplify:}

    (a)\;\log(d^4) - 2\log\sqrt{d} + 3\log(d^2)
    \log(d^4) - \log(\sqrt{d})^2 + \log(d^2)^3 \;=\;\log(d^4) - \log(d) + \log(d^6)

    . . =\; \log\left(\frac{d^4\cdot d^6}{d}\right) \;=\;\log(d^9) \;=\;9\log(d)


    (b)\;\frac{2\log(x^5) - 3\log(x^2)}{2\log(x^2)}
    \frac{\log(x^5)^2 - \log(x^2)^3}{\log(x^2)^2} \;=\; \frac{\log(x^{10}) - \log(x^6)}{\log(x^4)} \;=\; \frac{\log(\frac{x^{10}}{x^6})}{\log(x^4)} \;=\;\frac{\log(x^4)}{\log(x^4)} \;=\;1


    (c)\;2\log(p^5) - \log\sqrt[3]{p^9}
    \log(p^5)^2 - \log(p^9)^{\frac{1}{3}} \;=\;\log(p^{10}) - \log(p^3) \;=\;\log(p^7) \;=\;7\log(p)



    \text{3. Factor:}

    (a)\;5pq + 35pr
    5p(q + 7r)


    (b)\;12ab - 9bc + 6bd
    3b(4a-3c+2d)


    (c)\;5bc - 2bd + 5fc - 2fd

    b(5c-2d) + f(5c-2d) \;=\; (5c-2d)(b+f)
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