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) $0.0512$
B) $1.8572$
C) $0.2549$
D) $0.8293$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, $\log_{10} \frac{27}{4} = \log_{10} 27 - \log_{10} 4$. We know $\log_{10} 27 = 3 \log_{10} 3 \approx 3 \times 0.4771 = 1.4313$ and $\log_{10} 4 = 2 \log_{10} 2 \approx 2 \times 0.3010 = 0.6020$. Therefore, $\log_{10} \frac{27}{4} \approx 1.4313 - 0.6020 = 0.8293$.

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