Given $\log _ { 10 } 2 \approx 0.3010 \text { and } \log _ { 10 } 3 \approx 0.4771$ find the logarithm without using a calculator.
-$\log _ { 10 } \left( 18 ^ { 1 / 3 } \right)$
A) 0.5187
B) 0.4184
C) 1.0787
D) 0.7782

Question

Quizplus · Accepted Answer

The given expression can be simplified using logarithm properties: $\log _ { 10 } \left( 18 ^ { 1 / 3 } \right) = \frac{1}{3} \log _ { 10 } 18 = \frac{1}{3} \log _ { 10 } (2 \cdot 3^2) = \frac{1}{3} (\log _ { 10 } 2 + 2\log _ { 10 } 3) = \frac{1}{3} (0.3010 + 2 \cdot 0.4771) = \frac{1}{3} (0.3010 + 0.9542) = \frac{1}{3} \cdot 1.2552 = 0.4184.$

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