Use the properties of logarithms to evaluate $ln e ^ { 5 } - \ln e ^ { 4 }$ without a calculator.

A) $54\sqrt [ 4 ] { 5 }$
B) 9
C) 0
D) 1
E) $45\frac { 4 } { 5 }$

Question

Use the properties of logarithms to evaluate

ln e ^ { 5 } - \ln e ^ { 4 }

without a calculator.

A)

54\sqrt [ 4 ] { 5 }

B) 9
C) 0
D) 1
E)

45\frac { 4 } { 5 }

Simeon Oyemala · Accepted Answer

Final Answer : D, Explanation :   Using the property that   ln ⁡ a b = b ln ⁡ a \ln a ^ { b } = b \ln a ln a b = b ln a  , we can rewrite the expression as: ln ⁡ e 5 − ln ⁡ e 4 = 5 ln ⁡ e − 4 ln ⁡ e = 5 − 4 = 1 \ln e ^ { 5 } - \ln e ^ { 4 } = 5 \ln e - 4\ln e = 5 - 4 = 1 ln e 5 − ln e 4 = 5 ln e − 4 ln e = 5 − 4 = 1 Therefore, the answer is D) 1.

Use the properties of logarithms to evaluate $ln e ^ { 5 } - \ln e ^ { 4 }$ without a calculator.

A) $54\sqrt [ 4 ] { 5 }$
B) 9
C) 0
D) 1
E) $45\frac { 4 } { 5 }$

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Learning Objectives

Learning Objectives

Related questions

Use the properties of logarithms to evaluate ln⁡e5−ln⁡e4\ln e ^ { 5 } - \ln e ^ { 4 }lne5−lne4 without a calculator.A) 54\sqrt [ 4 ] { 5 }45​ B) 9C) 0D) 1E) 45\frac { 4 } { 5 }54​

Definitions

Learning Objectives

Learning Objectives

Related questions

Use the properties of logarithms to evaluate $ln e ^ { 5 } - \ln e ^ { 4 }$ without a calculator.

A) $54\sqrt [ 4 ] { 5 }$
B) 9
C) 0
D) 1
E) $45\frac { 4 } { 5 }$