Respuesta :
The value of In(e²) is 2.
A logarithm is the power to which a number must be raised in order to get some other number. For illustration, the base ten logarithm of 100 is 2(two), because ten raised to the power of two is [tex]100\ log_{100} = 2.[/tex]
This is an illustration of a base- ten logarithm. We call it a base ten logarithm because ten is the number that's raised to a power. The base unit is the number being raised to a power. There are logarithms using different base units. However, you could use two as a base unit, If you wanted. For case, the base two logarithm of eight is three, because two raised to the power of three equals eight . In general, you write log followed by the base number as a subscript. The most common logarithms are base 10 logarithms and natural logarithms; they've special memos.
In this case, e to the power of 2(two) is [tex]e^2[/tex].
thus, ln ([tex]e^2[/tex]) = 2(two)
Another way is using the property of logarithms(log) that says,
ln ([tex]a^b[/tex]) = b. ln (a)
In this case,
a = e
and
b = 2
Thus,
ln ([tex]e^2[/tex]) = 2(two)⋅ ln (e) = 2⋅1 = 2
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