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Thread: exponential equation (With pictures!)

  1. #1
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    exponential equation (With pictures!)

    This should just about sum it up.




    Thank you interent people!
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  2. #2
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    Quote Originally Posted by Vamz View Post
    This should just about sum it up.




    Thank you interent people!
    $\displaystyle f(x) = -2^{x - 1} + \frac{7}{2}$.

    To find the $\displaystyle x$ intercept, let $\displaystyle f(x) = 0$.


    So $\displaystyle -2^{x - 1} + \frac{7}{2} = 0$

    $\displaystyle 2^{x - 1} = \frac{7}{2}$

    $\displaystyle 2\cdot 2^{x - 1} = 7$

    $\displaystyle 2^{x} = 7$

    $\displaystyle \ln{(2^x)} = \ln{7}$

    $\displaystyle x\ln{2} = \ln{7}$

    $\displaystyle x = \frac{\ln{7}}{\ln{2}}$.
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    Quote Originally Posted by Prove It View Post
    $\displaystyle f(x) = -2^{x - 1} + \frac{7}{2}$.

    To find the $\displaystyle x$ intercept, let $\displaystyle f(x) = 0$.


    So $\displaystyle -2^{x - 1} + \frac{7}{2} = 0$

    $\displaystyle 2^{x - 1} = \frac{7}{2}$

    $\displaystyle 2\cdot 2^{x - 1} = 7$

    $\displaystyle 2^{x} = 7$ what happeend to ^(x-1) .. and that other 2?

    $\displaystyle \ln{(2^x)} = \ln{7}$

    $\displaystyle x\ln{2} = \ln{7}$

    $\displaystyle x = \frac{\ln{7}}{\ln{2}}$.

    Your final answer does not equal to ln(7)

    what I posted was what my teacher had in the answer key. I am assuming he's right... unless he was wrong!?
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  4. #4
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    You should know that

    $\displaystyle a^m \cdot a^n = a^{m + n}$.


    Here you have

    $\displaystyle 2^1 \cdot 2^{x - 1} = 2^{1 + x - 1} = 2^x$.


    And your teacher is wrong.

    Either s/he meant $\displaystyle \frac{\ln{7}}{\ln{2}}$ or s/he meant $\displaystyle \log_2{7}$.
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  5. #5
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    Thank you.

    You sir, are a smart cookie. And I'd give you one, but I wouldn't know where to begin contacting you.


    case closed.
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  6. #6
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    Quote Originally Posted by Vamz View Post
    Thank you.

    You sir, are a smart cookie. And I'd give you one, but ...
    Hallo,

    a personal remark: Before you start throwing cookies around you could instead press the $\displaystyle \boxed{\text{Thanks}}$-button. That's the kind of food we are living on here .

    EB
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