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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 $$6^{200}=\boxed{156}$$

- 4 years ago

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

- 4 years ago

How can we do it without using Log Tables?

- 4 years ago

Ya! Do U know?

- 2 years, 7 months ago

Thanks

- 4 years ago

Use logarithm.

- 4 years ago