(a) e^(-2 ln(5))

Step 1: Use the property of logarithms a*ln(b) = ln(b^a) to simplify the exponent:
-2 ln(5) = ln(5^-2)

Step 2: Substitute this back into the original expression:
e^(ln(5^-2))

Step 3: Use the property of logarithms e^ln(a) = a to simplify the expression:
5^-2 = 1/25

(b) ln(ln(e^e^3))

Step 1: Use the property of logarithms ln(e^a) = a to simplify the innermost expression:
ln(e^e^3) = e^3

Step 2: Substitute this back into the original expression:
ln(e^3)

Step 3: Again, use the property of logarithms ln(e^a) = a to simplify the expression:
e^3

Question

(a) e^(-2 ln(5))

Step 1: Use the property of logarithms a*ln(b) = ln(b^a) to simplify the exponent:
-2 ln(5) = ln(5^-2)

Step 2: Substitute this back into the original expression:
e^(ln(5^-2))

Step 3: Use the property of logarithms e^ln(a) = a to simplify the expression:
5^-2 = 1/25

(b) ln(ln(e^e^3))

Step 1: Use the property of logarithms ln(e^a) = a to simplify the innermost expression:
ln(e^e^3) = e^3

Step 2: Substitute this back into the original expression:
ln(e^3)

Step 3: Again, use the property of logarithms ln(e^a) = a to simplify the expression:
e^3

Knowee AI · Accepted Answer