Given $$\log _ { 10 } 2 = 0.3010 \text { and } \log _ { 10 } 3 = 0.4771 \text {, }$$ find the logarithm without using a calculator.
-$\log _ { 10 } 6$
A) $0.9542$
B) $0.7781$
C) $0.1436$
D) $0.903$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $\log _ { 10 } 6$ can be rewritten as $\log _ { 10 } (2 \times 3)$, which equals $\log _ { 10 } 2 + \log _ { 10 } 3$. Substituting the given values, we get $0.3010 + 0.4771 = 0.7781$.

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