Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator.
-$\log _ { 10 } \frac { 27 } { 4 }$
A) 0.8293
B) 1.8572
C) 0.2549
D) 0.0512

Question

Quizplus · Accepted Answer

$\log _ { 10 } \frac { 27 } { 4 } = \log _ { 10 } 27 - \log _ { 10 } 4 = 3\log _ { 10 } 3 - 2\log _ { 10 } 2 = 3(0.4771) - 2(0.3010) = 1.4313 - 0.6020 = 0.8293.$

Given log⁡102≈0.3010 and log⁡103≈0.4771\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771log10​2≈0.3010 and log10​3≈0.4771

Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$