Given $$\log _ { 10 } 2 = 0.3010 \text { and } \log _ { 10 } 3 = 0.4771 \text {, }$$ find the logarithm without using a calculator.
-$$\log _ { 10 } 72$$
A) 1.8572
B) 0.2549
C) 0.8616
D) 2.0333

Question

Quizplus · Accepted Answer

To find $\log_{10} 72$, we can express 72 as a product of its prime factors, which is $2^3 \times 3^2$. Then, using the properties of logarithms, we can write $\log_{10} 72$ as $\log_{10} (2^3 \times 3^2)$. Applying the logarithm properties further, this becomes $3\log_{10} 2 + 2\log_{10} 3$. Substituting the given values, we get $3(0.3010) + 2(0.4771) = 0.903 + 0.9542 = 1.8572$.

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