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Math Help - Solve the exponential equation algebraically?

  1. #1
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    Solve the exponential equation algebraically?

    Solve the exponential equation algebraically: -14 + 3e^x = 11

    So I think I move the -14 to the other side, so now I'm left with
    3e^x = 25
    What do i do next?
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  2. #2
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    Quote Originally Posted by tsmith View Post
    Solve the exponential equation algebraically: -14 + 3e^x = 11

    So I think I move the -14 to the other side, so now I'm left with
    3e^x = 25
    What do i do next?
    1. Divide both sides by 3
    2. Take the natural log of both sides. Do not use a decimal approximation
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  3. #3
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    Ok, so
    e^x = 25/3
    How do I find the natural log of both sides?
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  4. #4
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    Quote Originally Posted by tsmith View Post
    Ok, so
    e^x = 25/3
    How do I find the natural log of both sides?
    ln(x) = log_e(x)

    You don't need to unless you're making a decimal approximation. It is fine to say that x = ln \left(\frac{25}{3}\right) = 2\ln\left(\frac{5}{3}\right) = 2ln5 - ln3

    Note that I used the laws of logs to simplify. If you're teacher wants you to make a decimal approximation there should be a button marked ln on your calculator
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  5. #5
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    My teacher wants me to round the result to 3 decimal places. What do I type in the calculator?

    Thank you for your help, by the way
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  6. #6
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    2*ln(5) - ln(3)
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