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:

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestSince 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 \(6^{200}=\boxed{156}\)

Log in to reply

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

Log in to reply

How can we do it without using Log Tables?

Log in to reply

Ya! Do U know?

Log in to reply

Thanks

Log in to reply

Use logarithm.

Log in to reply