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Answer :
To evaluate or simplify the expression [tex]\( e^{\ln 114} \)[/tex], we can use a key property of exponents and logarithms.
The expression [tex]\( e^{\ln 114} \)[/tex] involves an exponential function with a natural logarithm. The property we use here is:
[tex]\[ e^{\ln x} = x \][/tex]
This property states that the exponential function [tex]\( e \)[/tex] and the natural logarithm [tex]\( \ln \)[/tex] are inverse operations. Specifically, applying [tex]\( \ln \)[/tex] and then [tex]\( e \)[/tex] (or vice versa) on a positive number [tex]\( x \)[/tex] returns the number [tex]\( x \)[/tex] itself.
In our case, [tex]\( x = 114 \)[/tex]. Therefore, when you simplify the expression [tex]\( e^{\ln 114} \)[/tex], you directly get:
[tex]\[ e^{\ln 114} = 114 \][/tex]
So, the simplified value of the expression is 114.
The expression [tex]\( e^{\ln 114} \)[/tex] involves an exponential function with a natural logarithm. The property we use here is:
[tex]\[ e^{\ln x} = x \][/tex]
This property states that the exponential function [tex]\( e \)[/tex] and the natural logarithm [tex]\( \ln \)[/tex] are inverse operations. Specifically, applying [tex]\( \ln \)[/tex] and then [tex]\( e \)[/tex] (or vice versa) on a positive number [tex]\( x \)[/tex] returns the number [tex]\( x \)[/tex] itself.
In our case, [tex]\( x = 114 \)[/tex]. Therefore, when you simplify the expression [tex]\( e^{\ln 114} \)[/tex], you directly get:
[tex]\[ e^{\ln 114} = 114 \][/tex]
So, the simplified value of the expression is 114.
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