Question

Simplify the following expressions;
ln e3
ln e2y

Answer 1

Answer:

ln e^3 =3

ln e^2y =2y

Step-by-step explanation:

The natural logarithm and the rational number e are inverse functions. This implies they neutralize or simply cancel out each other. In this case, the solution is simply the value in the exponent.

In general;

$lne^{x}=xlne=x$

Answer 2

Answer:

ln e3 = 3

ln e2y = 2y

Step-by-step explanation:

For ln e3

Using the formula ln(e^x) = X * ln (e) and transforming the expression , we get

3ln (e)

The natural log of e equals 1

So

3 x 1 = 3

For ln e2y

Using the formula ln(e^x) = X * ln (e) and transforming the expression , we get

2y ln (e)

Since The natural log of e equals 1

So

1 x 2y = 2y