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A few basic C2 log questions i cant seem to do.. help would be much appreciated watch

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    9) Given that y = 10^x, show that:
    a) y^2 = 100
    easy.. (10^x)^2 = (10^2)x = 100^x
    b) y/10 = 10^x-1
    any ideas how to show this one?

    14) Given that p = log_q 16 (q as the base), express the following in terms of p.
    a) log_q 2 don't know how to do this
    b) log_q 8q don't know how to do this either

    3) Solve, giving your answers as exact fractions, these simultaneous equations:

    8^y = 4^(2x+3)
    log_2 y = 4 + log_2 x
    equation 1: (2^3)y = (2^2)^(2x+3)
    2^3y = 2^(4x+6)
    3y = 4x + 6
    I've probably already gone wrong here. If I have, what was i supposed to do? and If i haven't, where do I go from here?


    THANK YOU! ANY help is appreciated. this is a chapter im struggling on quite a bit
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    (Original post by dumb maths student)
    Question.
    9b.
    y=10^x
    \frac{y}{10}=\frac{10^x}{10}=10^  {-1}10^x = 10^{x-1}

    14a
    Rules of logarithms:
    log_qa^b = blog_qa which you can apply to get blog2, and put it in terms of p.

    14b
    log(ab) = log(a) + log(b)
    apply it to log(8q)
    log8q = log(8) + log(q)
    log_qq=1 and you can use the rule in 14a as well to get an answer.

    3
    2^{2y}=2^{4x+6}
    therefore:
    2y=4x+6
    y=2x+3
    Equation 2:
    log_2(2x+3)=4+log_2x
    log_2(2x+3)=log_216+log_2x
    log_2(2x+3)=log_216x
    2x+3=16x

    Then solve.
    Ask if you need more help
 
 
 
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