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Logarithm function are the inverse of the exponential numbers.The simplified results of the given equation are,

[tex]ln_e=1[/tex]

[tex]ln_e2x=2x[/tex]

[tex]ln(1)=0[/tex]

What is the logarithm function?

Logarithm function are the inverse of the exponential numbers.

  • In the problem 1 the natural log function of [tex]e[/tex] is given. It is known as the log function of [tex]e[/tex] to the base [tex]e[/tex].According to the properties of the logarithm function. The value of the log function of e with base e is equal to the 1. Thus

                [tex]ln_e=1[/tex]

  • In the problem 2 the base of the log function is e. As the logarithm and the exponential function are inverses. In such function logarithm undoes the exponential and the result will be the same. Thus,

              [tex]ln_e2x=2x[/tex]

  • In the problem 3 the base of the log function e. The value of log function with 1 function is equal to the zero.Thus,

              [tex]ln(1)=0[/tex]

Hence the simplified results of the given equation are,

[tex]ln_e=1[/tex]

[tex]ln_e2x=2x[/tex]

[tex]ln(1)=0[/tex]

Learn more about the logarithm function here;

https://brainly.com/question/13473114

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