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Math Help - logarithmic functions

  1. #1
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    logarithmic functions

    right now, we're learning about logs functions and whatnot. i find it quite hard to understand. i hope that you can help me understand log functions better by showing a step by step procedure of how to solve these problems. hints and tips are much appreciated!<3


    solve for x.




    thankyouuu!
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  2. #2
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    Quote Originally Posted by ninjuhtime View Post
    right now, we're learning about logs functions and whatnot. i find it quite hard to understand. i hope that you can help me understand log functions better by showing a step by step procedure of how to solve these problems. hints and tips are much appreciated!<3


    solve for x.






    thankyouuu!


    #1

    e^{x+5}/e^5=e^{x+5-5}=e^x.

    so you have e^x=3

    Answer: x=ln3


    #3


    e^{2lnx-ln(x^2+x-3)}=1 Remember if something to the power something (for example a^b) equals 1 the power is 0. (If a^b=1 then b=0)


    So in your case 2lnx-ln(x^2+x-3)=0 Using the fact that 2lnx=lnx^2 you get lnx^2-ln(x^2+x-3)=0

    This means "contents" of the logarithms are the same so x^2=x^2+x-3


    Answer x=3


    Try to solve # 2 by yourself.
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  3. #3
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    thank you so much for the help! but what about the base e? does it affect the answer? also i learned from my teacher that e^x is supposed to equal something. when e to the power of any constant equals 0, right?
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  4. #4
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    Quote Originally Posted by ninjuhtime View Post
    thank you so much for the help! but what about the base e? does it affect the answer? also i learned from my teacher that e^x is supposed to equal something. when e to the power of any constant equals 0, right?

    Base is included in Ln another words, Log with base e is Ln. Remember treat e as a number, it is just 2.73...... so of course e^x should equal something and that something depends on x. e^3=e*e*e, if power is x it will be a product of e x times. No it is not right e^{any constant} is not zero. Only power minus infinity makes it zero. Probably your teacher meant derivative....
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