Evaluate the expression without using a calculator. \(\displaystyle{e}^{{{2}{\ln{{7}}}}}\)

David Rodgers

David Rodgers

Answered question

2022-04-03

Evaluate the expression without using a calculator.
e2ln7

Answer & Explanation

delai59qk

delai59qk

Beginner2022-04-04Added 8 answers

Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to perform arithmetic operation on them. Multiplication and division can be written in form of addition and subtraction while operating logarithms.
There are various rules involved in performing logarithmic operations, some required for question are as follows
Product rule logamn=logam+logan
Power rule logaxn=nlogax
The given expression is e2ln7 . Let the expression be equal to y. Now take log on both sides to solve the equation
ln(e2ln7)=lny
2ln7lne=lny,(using  lnxn=nlnx)
2ln7=lny,(  using  ln(e)=1)
ln(72)=lny,(  using power rule)
7y=y,(  taking antilog on both sides)
y=49
Therefore, value of e2ln7 is equal to 49

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