Basic Maths and Logarithm
Number of Digits
JEE Main
Grade 11
Question:
Given $\log_{10} 2 = 0.3010$ and $\log_{10} 3 = 0.4771$, the number of digits in $6^{20}$ is _____.
Step-by-Step Solution
Key Concept: $\log_{10}(6^{20}) = 20 \log_{10} 6 = 20(\log_{10} 2 + \log_{10} 3) = 20(0.3010 + 0.4771) = 20 \times 0.7781 = 15.562$. Number of digits $= \lfloor 15.562 \rfloor + 1 = 16$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 16