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Number of digits in Exponentiation

How to find Number of digits in Exponentiation like number of digits in 6 ^ 200 or 74 ^100

Note by Mayank Kaushik
4 years ago

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Since we write our numbers in base 10, we can determine the number of digits by finding our number as an equivalent power of 10. ie:

\(10^x=6^{200}\)

\(log_{10}(10^x)=log_{10}(6^{200})\)

\(x=200log_{10}(6)\)

\(x \approx 155.63\)

Since our answer is going to be a whole number (as it is an integer raised to a positive integer power), we can check a few examples and see that we need to round up to get the solution:

Number of digits of \(6^{200}=\boxed{156}\)

Ryan Carson - 4 years ago

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In term of a formula, the number of digits of \(n\) is equal to \(\lfloor \log_{10} n \rfloor + 1\).

Mike Kong - 4 years ago

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How can we do it without using Log Tables?

Akshat Jain - 4 years ago

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Ya! Do U know?

Swapnil Das - 2 years, 7 months ago

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Thanks

Mayank Kaushik - 4 years ago

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Use logarithm.

Aditya Parson - 4 years ago

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