Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator.
-$\log _ { 10 } 24$
A) 0.4308
B) 1.3801
C) 1.7323
D) 0.5044

Question

Quizplus · Accepted Answer

The logarithm $\log _ { 10 } 24$ can be simplified using the properties of logarithms. Since $24 = 2^3 \times 3$, we can write $\log _ { 10 } 24$ as $\log _ { 10 } (2^3 \times 3)$. Using the properties of logarithms, this becomes $3\log _ { 10 } 2 + \log _ { 10 } 3$. Substituting the given values, we get $3(0.3010) + 0.4771 = 0.9030 + 0.4771 = 1.3801$.

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