PLE 4 Evaluate each natural logarithmic expression (a) In e (b) In (c) In 1 (d)

Question

PLE 4 Evaluate each natural logarithmic expression (a) In e (b) In (c) In 1 (d) In Ve Strategy Since the base is e in each case, we will ask "To what power must e be raised to get the given number? Why That power is the value of the logarithmic expression Solution (a) In e 1 Ask: To what power must we raise e to get e?" Since e -e, the answer is: the 1st power ?" Since e-2·1, the answer is: the-2 power Ask: "To what power must we raise e to get Ask·"To what power must we raise e to get i?" Since eo-1, the answer is: the 0 power, Ask: To what power must we raise o to get V@ Since e, the answer is: the power (c) In 1-0 (a) n e Self Check Evaluate each expression. (a) In es (b) In 1 (c) In V

Explanation / Answer

a) ln e = 1

b) ln e^2 = 2 ln e = 2

c) ln 1 = 0

d) ln sqrt e = ln e^1/2 = 1/2

2)  

a) ln e^5

= 5 ln e = 5

b) ln (1/e)

= ln e^-1

= -1

c) ln cube root (e)

= ln (e)^1/3

= 1/3

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