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Math Help - algebra need for 2moz

  1. #1
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    algebra need for 2moz

    a) given that 2^x = 1/[rt2] and 2^y = 4[rt2]
    find the exact value of x and the exact value of x

    b) given that 4^x = 8^(2-x) find the value of x

    c) given that3^x = 9^(y-1) show that x = 2y-2
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    I'll start you off
    Quote Originally Posted by kls7162 View Post
    a) given that 2^x = 1/[rt2] and 2^y = 4[rt2]
    find the exact value of x and the exact value of y
    2^x = \frac 1{\sqrt{2}}

    take log to the base 2 of both sides:

    \Rightarrow \log_2 2^x = \log_2 \left( \frac 1{\sqrt{2}}\right)

    \Rightarrow x \log_2 2 = \log_2 \left( \frac 1{\sqrt{2}}\right)


    2^y = 4 \sqrt {2}

    do the same thing here:


    b) given that 4^x = 8^(2-x) find the value of x
    note that
    4 = 2^2 and 8 = 2^3

    So we have \left( 2^2 \right)^x = \left( 2^3 \right)^{2 - x}

    now continue


    c) given that3^x = 9^(y-1) show that x = 2y-2
    similarly here, 3^x = \left( 3^2 \right)^{y - 1}

    now continue
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