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Math Help - indices - help!

  1. #1
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    indices - help!

    I have many questions that I need help with.

    1. Express 27 (to the power of x) in the form 3
    (to the power of ax) where a is an integer to be found.

    1(ii). hence solve the equation 3 (to the power of x) = 27 (to the power of x)

    2. √90 in the form a√10 where a is an integer

    2(ii). Express (5-2
    √3) in the form b+c√3 where b and c are integers

    3(i). Express 15/2-√2 in the form p+q√2

    3(ii). Express √8+√2 / √8-√2 as a single fraction

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  2. #2
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    Quote Originally Posted by notepad View Post
    I have many questions that I need help with.

    1. Express 27 (to the power of x) in the form 3
    (to the power of ax) where a is an integer to be found.

    1(ii). hence solve the equation 3 (to the power of x) = 27 (to the power of x)


    I'll try to interpret what you want, but I'm afraid something's lost in the translation. You may want to try and restate this one.

    27^x=3^{ax}

    3^{3x}=3^{ax}

    3x=ax

    3=a
    Quote Originally Posted by notepad View Post
    2. √90 in the form a√10 where a is an integer


    \sqrt{90}=\sqrt{9\cdot10}=3\sqrt{10}

    Quote Originally Posted by notepad View Post

    2(ii). Express (5-2 √3) in the form b+c√3 where b and c are integers


    (5-2\sqrt{3})^2=25-20\sqrt{3}+12=37-20\sqrt{3}

    Quote Originally Posted by notepad View Post
    3(i). Express 15/2-√2 in the form p+q√2


    \frac{15}{2-\sqrt{2}}\cdot\frac{2+\sqrt{2}}{2+\sqrt{2}}=\frac{  30+15\sqrt{2}}{4-2}=15+\frac{15}{2}\sqrt{2}

    Quote Originally Posted by notepad View Post
    3(ii). Express √8+√2 / √8-√2 as a single fraction

    \frac{\sqrt{8}+\sqrt{2}}{\sqrt{8}-\sqrt{2}}\cdot\frac{\sqrt{8}+\sqrt{2}}{\sqrt{8}+\s  qrt{2}}=\frac{8+2\sqrt{16}+2}{8-4}=\frac{8+8+2}{4}=\frac{18}{4}=\frac{9}{2}
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