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

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $\log _ { 16 } \frac { 3 } { 4 } = \log _ { 16 } 3 - \log _ { 16 } 4 = 0.3962 - 0.5000 = -0.1038$.

Use log⁡164=0.5000\log _ { 16 } 4 = 0.5000log16​4=0.5000 log⁡163≈0.3962\log _ { 16 } 3 \approx 0.3962log16​3≈0.3962

Use $\log _ { 16 } 4 = 0.5000$ $\log _ { 16 } 3 \approx 0.3962$