Doubt! Please help!

Find the number of digits in $\large2^{2^{22}}$ ?

#Algebra #NumberTheory #RMO

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Math	Appears 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

1262612

Dev Sharma - 5 years, 6 months ago

Actually I got the answer but according to my book answer key I was wrong so....Thanks

naitik sanghavi - 5 years, 6 months ago

@Dev Sharma DevBut how will you find the number of digits without computing $\large2^{22}$ if it is asked in exam?

naitik sanghavi - 5 years, 6 months ago

U may assume the no. Of digits of a number be x. Let the number be a^b. So 10^(x-1) = a^b X-1 = blog(a) [log with base 10] X = blog(a) +1 For convenience, X = [blog(a)] +1 So 2^22 has [22log(2)] +1 digits.similarly following can be calculat ed

Aditya Narayan Sharma - 5 years, 6 months ago

@Aditya Narayan Sharma – How to apply here .here it will become 2^22 log(2) then we have to apply log again then do antilog.after doing this I got answer 447 .is it right??????

Anshul Sanghi - 5 years, 5 months ago

@Calvin Lin Please help me with this!

naitik sanghavi - 5 years, 6 months ago

Math	Appears 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}`	$\boxed{123}$