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Math Help - help with logs

  1. #1
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    help with logs

    I have two functions

    f(x)= 9^x and

    g(x)= log_{3}(x)


    I am asked to write h(x) = (f o g)(x). I thought this should be

    9^ (log_{3}(x))

    Is this correct? How can we solve this? And the book is asking for a quadratic function, how can this be done? Thanks!
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by andres View Post
    I have two functions

    f(x)= 9^x and

    g(x)= log_{3}(x)


    I am asked to write h(x) = (f o g)(x). I thought this should be

    9^ (log_{3}(x))

    Is this correct? How can we solve this? And the book is asking for a quadratic function, how can this be done? Thanks!
    (f\, o\, g)(x) = f[g(x)] = 9^{log_3(x)} as you said

    Here it's important to notice that 9 = 3^2

    Using the laws of exponents and logs this simplifies to:

    (f\, o\, g)(x) = (3^2)^{log_3(x)} = 3^{2log_3(x)} = 3^{log_3(x^2)} = x^2
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  3. #3
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    Thank you so much. I just have a last question, the book is asking for a quadratic function h(x)=ax^2+bx+c. In this case, will x^2 be considered a quadratic function?
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  4. #4
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    e^(i*pi)'s Avatar
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    Yes, x^2 is a quadratic function, it just happens that b = c = 0. It's unsual though
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  5. #5
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    Thank you again!
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