Simplify ln(e^2) - 4ln(1/e)

Using log rules, we can simplify the equation as follows: Firstly log(xa) = alog(x) implies that ln(e2) = 2ln(e). Next loga(a) = 1 implies 2ln(e) = 21 = 2 [Since the natural logarithm ln is equivalent to loge]. So ln(e2) = 2. Following this ln(1/e) = ln(e-1), which from the previous rule we can see ln(e-1) = -ln(e). Lastly we know ln(e) = 1, so -4*-ln(e) = -4*-1 = 4. So -4ln(1/e) = 4. Therefore ln(e2) - 4ln(1/e) = 2 + 4 = 6

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Answered by Mark J. Maths tutor

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