What is the value of lnsqrt [5](e^2)

<p> To start, remember that square-root takes precedence over exponentiation in operations. The term inside the natural log is namely: (5 √e^2). It would be inappropriate to excessively complicate this expression, because √e^2, by concept of the square root or previously speaking radical, simply just equals e. Because any positive number greater than 0, when square rooted and squared -- repeating operations actually that are inverse of each other--would come out equal to the original value. Hence, √e^2 = e, and 5e is the valued term of inside of the natural logarithm. Now, if we recall our logarithm rules or natural logarithm rules in particular, a coefficient multiplying the input of a natural logarithm can be rewritten as it's own natural log multiplied with the original log and both added together. This manipulation of course comes from properties of logarithms, and thus in general in this case ln(a * b) = ln(a) + ln(b), so ln(5e) = ln(5) + ln(e). Finally, recognize that ln(e) = 1 because of the definition of a natural log in the context of e:=2.72 approximation. Therefore,toEqual unitsl sum is indeed ln(5) + 1.</p>