Waste less time on Facebook — follow Brilliant.
×

Going way too up

Find the number of digits of the number \(2^{2^{22}} \).

Note by Subham Subian
11 months, 4 weeks ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Here, \(2^{2^{22}}\) = x , Taking \(log_{10}\) on both sides we get \(2^{22} log _{10}2 = log_{10}x\)

Now \(2^{22} = y\)

\(log_{10}y = 22 log_{10}2\)

Hence log 2 = 0.301 hence \(log _{10} y = 22 * 0.301\)

y = 10^{6.62}

Y has 7 digits in it.

Now \(y \lesssim 10^{7}\)

Hence Now \(10^7 x 0.301\) = \(log_{10}x\)

\( 3010000\) = \(log_{10}x

hence x = \(10^{3010000}\)

is it the answer?

Or 3010000 digits?

Md Zuhair - 11 months, 3 weeks ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...