Log

Algebra Level 2

Given that 0.477 < log ⁡ 10 3 < 0.478 0.477 < \log_{10} 3 < 0.478 , how many digits are there in the decimal expansion of 3 40 3 ^ {40} ?


The answer is 20.

Abhinandan Sharma by Abhinandan Sharma , 20, India

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1 solution

Abhinandan Sharma
Jun 15, 2017

Simple Log3=. 477 so 3=10^.4777 3^40=10^19.080 So there would be 19 digits.

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Note: 1 0 1 . 1 10 ^ 1.1 has 2 digits. You needed to take the ceiling function .

Calvin Lin Staff - 3 years, 8 months ago

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