Question

If In a = 2, ln b = 3, and ln c = 5, evaluate the following:

¹ (²³) =
1c3
(a) In
(b) In √6-³c²a-1
(c)
In(a¹b¹)
In (be) ¹
=
(d) (ln c−²) (In
-12
=
10100
5
8
64
11/12
4
¹ = |
✓
OT

Answer 1

To evaluate the given expressions, we substitute the given values and perform the necessary calculations. (a) ln(a) = 0.693. (b) The expression is undefined. (c) ln(a¹b¹) = ln(6) = 1.792. (d) (ln(c)-²)(In(-12)) = 95.574.

Step-by-step explanation:

To evaluate the given expressions, we need to substitute the given values into the given equations and perform the necessary calculations.

(a) ln(a)

Substituting a = 2, we have ln(2) = 0.693 (approximately).

(b) ln(√6-³c²a-1)

Substituting a = 2, c = 5, we have ln(√6-³(5)²(2)-1)

= ln(√6-(375))

= ln(√(-369))

Since the argument inside the ln function is negative, the expression is undefined.

(c) ln(a¹b¹)

Substituting a = 2, ln(b) = 3, we have ln(2¹(3)¹)

= ln(2(3))

= ln(6)

Approximately, ln(6) = 1.792 (rounded).

(d) (ln(c)-²)(In(-12)

Substituting ln(c) = 5, we have (ln(5)-²)(In(-12))

= (5-²)(In(-12))

= (25-²)(In(-12))

= 23(4.158)

Approximately, 23(4.158) = 95.574 (rounded).