Respuesta :
ln e³ = 3, by definition and properties of logarithm.
What is Logarithm?
- The opposite of exponentiation is the logarithm.
- This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
- A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Now,
As seen by the definition of logarithms, [tex]log_b(a)=x[/tex]
In case of natural logarithm, b = e, i.e., [tex]log_e(a)[/tex] = ln (a) = x
In the question, ln (e)³, a = e
By property of logarithms, [tex]log_b(a^m) = m(log_b(a))[/tex] ,
=> 3 (ln (e)) = 3 [tex]log_e(e)[/tex]
Since, [tex]log_e(e)[/tex] = 1, ln (e)³ = 3 (1) = 3.
Hence, ln e³ = 3, by definition and properties of logarithm.
To learn more about logarithms, refer to the link: brainly.com/question/25710806
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