Jamaal
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Jamaal asked in Science & MathematicsMathematics · 1 decade ago

9^a*3^c= 177,147, 2a+c=x Find the value of x?

9 to the a power times 3 to the c power= 177, 147

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  • 1 decade ago
    Favorite Answer

    9^a * 3^c = 177147

    (3^2)^a * 3^c = 177147

    3^(2a) * 3^c = 177147

    3^(2a + c) = 177147

    3^(2a + c) = 3^11

    therefore

    2a + c = 11

    x = 11

  • 1 decade ago

    9^a3^c = (3^(2a))(3^c) = 3^(2a+c) = 177147 = 3^11

    from above

    2a+c = 11

    2a+c = x

    => x = 11

  • 1 decade ago

    9 ^a * 3^c = 177,147

    take log on both sides (note log a^ b = bloga ; log xy = logx + logy)

    alog9 + clog3 = log 177,147

    alog (3^2) + clog3 = log177,147

    2alog3 + clog3 = log 177,147

    2a + c = log177,147/log3 = log (3^11)/log 3 = 11log3/log3 = 11

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