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

Using log rules, we can simplify the equation as follows: Firstly log(x^a) = alog(x) implies that ln(e²) = 2ln(e). Next log_a(a) = 1 implies 2ln(e) = 21 = 2 [Since the natural logarithm ln is equivalent to log_e]. 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