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Math Help - exponential and logarithmic functions

  1. #1
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    exponential and logarithmic functions

    I am working with this problem:

    6 + e^0.5 t = 8

    e^0.5 t = 2

    0.5 t = ln 2

    t = 2 ln 2 I am confused as to how my book got 2 on the right side.

    I come up with 1/2. I am wanting to divide each side by 1/2 but the book states to multiply each side by 2. I do not understand.

    could someone help please?

    thanks!
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  2. #2
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     6 + e^{\frac{1}{2}t} = 8

     e^{\frac{1}{2}t} = 2

    NOW, WE TAKE THE NATURAL LOG OF BOTH SIDES AS THE NEXT STEP WILL SHOW:

     \ln({e^{\frac{1}{2}t}}) = \ln{2}

     \frac{1}{2}t = \ln{2}

     t = 2\ln{2}


    This is what you should know so you can do these problems:

     e^{\ln{x}} = x

     \ln{e^x} = x

    So,  e^{\ln{x}} = \ln{e^x} = x .

    Good luck!
    -Andy
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  3. #3
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    Quote Originally Posted by robasc View Post
    I am working with this problem:

    ...

    I am wanting to divide each side by 1/2 but the book states to multiply each side by 2. I do not understand.

    could someone help please?

    thanks!
    Dividing by \frac12 is exactly the same as multiplying by 2.
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  4. #4
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    so in other words, yo multiply by the reciprocal
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