evaluate the expression without using a calculator.\n\nin ( e ^ { 6 } )\n\n( ln e ^ { 6 } = )
evaluate the expression without using a calculator.\n\nin ( e ^ { 6 } )\n\n( ln e ^ { 6 } = )
Answer
Explanation:
Step1: Use the logarithm power rule
The logarithm power rule is (\ln a^b = b\ln a). For the expression (\ln e^{6}), here (a = e) and (b = 6). So, (\ln e^{6}=6\ln e).
Step2: Use the property of natural logarithm
We know that the natural logarithm (\ln x) has the property (\ln e = 1) (since (y=\ln x) is the inverse function of (y = e^{x}), and (e^{1}=e)). Substituting (\ln e = 1) into (6\ln e), we get (6\times1).
Answer:
(6)