Answer:In(e^3 x^4) simplifies to 3x^4.
Explanation:
In(e^3 x^4) simplifies to just 3x^4, since the natural logarithm (ln or In) and exponential function (e^x) are inverse functions of each other.
To see why, recall that ln(e^y) = y for any real number y, and e^(ln x) = x for any positive real number x. Therefore:
ln(e^3 x^4) = 3x^4 ln(e) (using the rule ln(xy) = ln(x) + ln(y) and ln(e) = 1)
= 3x^4 * 1 (since ln(e) = 1)
= 3x^4