Use the properties of logarithms to evaluate $3\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }$ without a calculator.

A) -6
B) -8
C) $18\frac { 1 } { 8 }$
D) 6
E) $32\frac { 3 } { 2 }$

Question

Use the properties of logarithms to evaluate

3\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }

without a calculator.

A) -6
B) -8
C)

18\frac { 1 } { 8 }

D) 6
E)

32\frac { 3 } { 2 }

Daisy Shumake · Accepted Answer

Final Answer : A, Explanation :   Using the properties of logarithms,   log ⁡ 10 ( 1 100 ) 3 \log _ { 10 } \left( \frac { 1 } { 100 } ight) ^ { 3 } lo g 10 ​ ( 100 1 ​ ) 3   can be simplified as   3 log ⁡ 10 ( 1 100 ) 3 \log _ { 10 } \left( \frac { 1 } { 100 } ight) 3 lo g 10 ​ ( 100 1 ​ )  . Since   log ⁡ 10 100 = 2 \log _ { 10 } 100 = 2 lo g 10 ​ 100 = 2  , and   log ⁡ 10 ( 1 100 ) = − 2 \log _ { 10 } \left( \frac { 1 } { 100 } ight) = -2 lo g 10 ​ ( 100 1 ​ ) = − 2  , the expression simplifies to   3 × − 2 = − 6 3 	imes -2 = -6 3 × − 2 = − 6  .

Use the properties of logarithms to evaluate $3\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }$ without a calculator.

A) -6
B) -8
C) $18\frac { 1 } { 8 }$
D) 6
E) $32\frac { 3 } { 2 }$

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Learning Objectives

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Use the properties of logarithms to evaluate log⁡10(1100) 3\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }log10​(1001​) 3 without a calculator.A) -6B) -8C) 18\frac { 1 } { 8 }81​ D) 6E) 32\frac { 3 } { 2 }23​

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Learning Objectives

Learning Objectives

Related questions

Use the properties of logarithms to evaluate $3\log _ { 10 } \left( \frac { 1 } { 100 } \right) ^ { 3 }$ without a calculator.

A) -6
B) -8
C) $18\frac { 1 } { 8 }$
D) 6
E) $32\frac { 3 } { 2 }$