Use log ⁡ 16 4 = 0.5000 \log _ { 16 } 4 = 0.5000 lo g 16 4 = 0.5000 , log ⁡ 16 3 ≈ 0.3962 \log _ { 16 } 3 \approx 0.3962 lo g 16 3 ≈ 0.3962 , and the properties of logarithms to approximate log ⁡ 16 3 4 \log _ { 16 } \frac { 3 } { 4 } lo g 16 4 3 to four decimal places. Do not use a calculator.A) 1.8200 1.8200 1.8200 B) − 0.1038 - 0.1038 − 0.1038 C) − 0.4024 - 0.4024 − 0.4024 D) 0.7925 0.7925 0.7925 E) − 1.5230 - 1.5230 − 1.5230

Question

Use   log ⁡ 16 4 = 0.5000 \log _ { 16 } 4 = 0.5000 lo g 16 ​ 4 = 0.5000   ,   log ⁡ 16 3 ≈ 0.3962 \log _ { 16 } 3 \approx 0.3962 lo g 16 ​ 3 ≈ 0.3962   , and the properties of logarithms to approximate   log ⁡ 16 3 4 \log _ { 16 } \frac { 3 } { 4 } lo g 16 ​ 4 3 ​   to four decimal places. Do not use a calculator.A)    1.8200 1.8200 1.8200 B)    − 0.1038 - 0.1038 − 0.1038 C)    − 0.4024 - 0.4024 − 0.4024 D)    0.7925 0.7925 0.7925 E)    − 1.5230 - 1.5230 − 1.5230

Jomar Mallannao · Accepted Answer

Final Answer : B, Explanation :   Using the properties of logarithms,   log ⁡ 16 3 4 = log ⁡ 16 3 − log ⁡ 16 4 = 0.3962 − 0.5000 = − 0.1038 \log _ { 16 } \frac { 3 } { 4 } = \log _ { 16 } 3 - \log _ { 16 } 4 = 0.3962 - 0.5000 = -0.1038 lo g 16 ​ 4 3 ​ = lo g 16 ​ 3 − lo g 16 ​ 4 = 0.3962 − 0.5000 = − 0.1038  .

Use $log _ { 16 } 4 = 0.5000$ , $log⁡163≈0.3962\log _ { 16 } 3 \approx 0.3962$ , and the properties of logarithms to approximate $log⁡1634\log _ { 16 } \frac { 3 } { 4 }$ to four decimal places. Do not use a calculator.

A) $1.8200$
B) $- 0.1038$
C) $- 0.4024$
D) $0.7925$
E) $- 1.5230$

Definitions

Learning Objectives

Learning Objectives

Related questions