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Math Help - Solving for x in an exponential function

  1. #1
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    Solving for x in an exponential function

    I've been struggling on figuring out these kinds of problems when I need to set f(x) equal to zero and solve for x.

    f(x)={12(1.5^x)}+{12(0.5^x)}

    Here's my thought process:

    1) 0={12(1.5^x)}+{12(0.5^x)}

    2) \frac{0}{12}=\frac{12(1.5^x)}{12}+\frac{12(0.5^x)}  {12}

    3) {0}={(1.5^x)}+(0.5^x)}

    4) {0}={(1.5^x)}+(0.5^x)}; here's where my intuition breaks down. I want to take the log of both sides but I can't due to the zero! Am I going about this kind of problem wrong from the beginning?
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  2. #2
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    Re: Solving for x in an exponential function

    1.5^x + 0.5^x = 0 has no solution ... why?
    Thanks from BAdhi and AZach
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  3. #3
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    Re: Solving for x in an exponential function

    No logs of 0. Oh, so this is why there's always a vertical asymptote at x=0 for logarithmic functions.
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    Re: Solving for x in an exponential function

    Quote Originally Posted by AZach View Post
    No logs of 0. Oh, so this is why there's always a vertical asymptote at x=0 for logarithmic functions.
    no ...

    1.5^x > 0

    0.5^x > 0

    how can you add two positives and get 0 ?
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