MATH SOLVE

2 months ago

Q:
# Evaluate the expression. If necessary, round to the nearest hundredth. ln 0

Accepted Solution

A:

well, a logarithmic expression is just an exponential expression written from the point of the exponent.

now, ln is just a shorthand for the logarithm with a base "e" or euler's constant, so-called the "natural logarithm", now, let's use the exponential version of that here, and let's say equals an constant exponent of "k",

[tex]\bf \textit{exponential form of a logarithm}\\\\ log_{{ a}}{{ b}}=y \implies {{ a}}^y={{ b}}\qquad\qquad % exponential notation 2nd form {{ a}}^y={{ b}}\implies log_{{ a}}{{ b}}=y\\\\ -------------------------------\\\\ ln(0)=k\implies log_e(0)=k\implies e^k=0[/tex]

now, look closely, what "k" value, what exponent, negative or fraction or positive, will ever make "e" to 0?Β none, so one can say is "undefined".

now, ln is just a shorthand for the logarithm with a base "e" or euler's constant, so-called the "natural logarithm", now, let's use the exponential version of that here, and let's say equals an constant exponent of "k",

[tex]\bf \textit{exponential form of a logarithm}\\\\ log_{{ a}}{{ b}}=y \implies {{ a}}^y={{ b}}\qquad\qquad % exponential notation 2nd form {{ a}}^y={{ b}}\implies log_{{ a}}{{ b}}=y\\\\ -------------------------------\\\\ ln(0)=k\implies log_e(0)=k\implies e^k=0[/tex]

now, look closely, what "k" value, what exponent, negative or fraction or positive, will ever make "e" to 0?Β none, so one can say is "undefined".