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Math Help - Log Sketches

  1. #1
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    Question Log Sketches



    Given the pts A (a, log a) and B (b, log b) on the curve y= log x, a is not equal to b.

    (c) Given point Q is directly to the left of M on y = log x

    (i) Find the coordinates of Q.

    (ii) Show that x^2 with the base of Q = ab

    For (i), I was wondering: For the y coordinate, I found it to be log ((a+b)/2). I was wondering how the answer becomes 1/2log ab (thatís what my teacher got). If itís wrong, could someone please show me how to simplify it?

    For (ii), I have no clue how to solve the question. Could someone please guide me?

    N.B. For all the logs in this question, they are in base 10. Sorry
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post

    Given the pts A (a, log a) and B (b, log b) on the curve y= log x, a is not equal to b.

    (c) Given point Q is directly to the left of M on y = log x

    (i) Find the coordinates of Q.

    (ii) Show that x^2 with the base of Q = ab

    For (i), I was wondering: For the y coordinate, I found it to be log ((a+b)/2). I was wondering how the answer becomes 1/2log ab (thatís what my teacher got). If itís wrong, could someone please show me how to simplify it?

    For (ii), I have no clue how to solve the question. Could someone please guide me?

    N.B. For all the logs in this question, they are in base 10. Sorry
    M is the midpoint of A and B. Use the midpoint formula:

    M\left(\dfrac{a+b}2\ ,\ \dfrac{\log a + \log b}{2}  \right)

    yields:

    M\left(\dfrac{a+b}2\ ,\ \dfrac{\log(a\cdot b)}{2}  \right)

    M\left(\dfrac{a+b}2\ ,\ \log(\sqrt{a\cdot b)}  \right)

    Maybe you can use the last line to solve (ii)
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