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Algebra Level 3

If $\log 2$ is approximately equals to $0.30103$ correct to 5 decimal places, what is the number of digits for the number ${5}^{20}$ ?

The answer is 14.

1 solution

Mehul Arora
Jun 16, 2015

$log 5=log 10- log 2$

$log 5= 1-0.30103 = 0.698 (approx)$

Hence, number of digits in ${5}^{20}$ = Floorfunction of $0.698 \times 20$

$=14$

Moderator note:

Note that Number of digits of $N$ is not equal to $\lceil \log_{10} N \rceil$ . Instead, it is equal to $\lfloor \log_{10} N \rfloor + 1$ . E.g. take $N = 10$ .

I blv the question has been wrongly asked. They should have asked the value of log 5 ^20, rather than the digita

Alok Kumar - 5 years, 12 months ago

It asks for the number of digits of $5 ^ {20}$ .

Calvin Lin Staff - 5 years, 11 months ago

Comment:- Sorry guys, I do not know how to latex the Ceiling function. :/

Mehul Arora - 5 years, 12 months ago

Use the \lceil and \rceil commands : $\lceil 0.698 \times 20 \rceil$

Luís Sequeira - 5 years, 11 months ago

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The answer is 14.

1 solution

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