Question

Use the properties relating exponential and logarithmic functions to simplify each expression. (a) e^(2 ln (2)) = (b) (1/6) ln (e^(-2)) =

Answer 1

We used properties of exponentials and logarithms to simplify to 4 and (1/6) ln

Step-by-step explanation:

We will simplify each expression by applying the properties of exponential functions and natural logarithms.

Part (a)

For the expression e2 ln(2), we use the property that states if you have an exponent as a logarithm (ln), you can simplify it by raising the base of the logarithm (e) to the power inside the logarithm.

So, e2 ln(2) = eln(22) = 22 = 4, as e and ln are inverse functions and cancel each other out.

Part (b)

Now for (1/6) ln(e-2), applying the rules of natural logarithms, the expression simplifies to:

(1/6) * (-2) = -1/3, because ln(ex) = x.