×

# 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
3 years, 9 months ago

Sort by:

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 $$6^{200}=\boxed{156}$$ · 3 years, 9 months ago

In term of a formula, the number of digits of $$n$$ is equal to $$\lfloor \log_{10} n \rfloor + 1$$. · 3 years, 9 months ago

How can we do it without using Log Tables? · 3 years, 9 months ago

Ya! Do U know? · 2 years, 4 months ago

Thanks · 3 years, 9 months ago