Given $$\log _ { 10 } 2 = 0.3010 \text { and } \log _ { 10 } 3 = 0.4771 \text {, }$$ find the logarithm without using a calculator.
-$$\log _ { 10 } \frac { 9 } { 8 }$$
A) 0.1992
B) 0.0512
C) 2.0333
D) 0.8293

Question

Quizplus · Accepted Answer

The given expression can be simplified using logarithm properties: $$\log _ { 10 } \frac { 9 } { 8 } = \log _ { 10 } 9 - \log _ { 10 } 8 = 2\log _ { 10 } 3 - 3\log _ { 10 } 2 = 2(0.4771) - 3(0.3010) = 0.9542 - 0.9030 = 0.0512.$$

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

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