Logs Question (2 Viewers)

[brahmin]

Can anyone do this??

We know that 2^10 = 1024 so that 2^10 can be represented as a 4 digit numeral.

How many digits are there in 2^1000 when written as a numeral?

 

[ohexploitable]

Just stick it in your calculator?

I got 31 digits.

 

[brahmin]

hmmm think ur meant to work it out though

apparently its only a one mark question too so either theres a really easy method im just not seeing, or its worded wrong

 

[ohexploitable]

If it's one mark then you just write "31".

 

[brahmin]

yeh but my calculator cant work it out ive got one of the older casios

 

[NewiJapper]

get a better one then...

 

[Drongoski]

Can anyone do this??

We know that 2^10 = 1024 so that 2^10 can be represented as a 4 digit numeral.

How many digits are there in 2^1000 when written as a numeral?

I did a similar one last year.

It is equal to log₁₀ 2¹⁰⁰⁰ = [1000 log₁₀ 2] + 1

= [1000 x 0.30102999 . . .] = 301 + 1 = the nearest whole no + 1

= 302

Edit

Corrected as above

 

[Drongoski]

Dragonmaster

 

[nonsenseTM]

isn't it 302 cos the log thing shows 10^(1000 x 0.30102999 . . .)=2^1000=10^(301.0299) which has 302 digits , ie 10^1.1 is a 2 digit no.

 

[cutemouse]

This is from the 2U 2003 or 2005 HSC (IIRC). The answer is 302. You need to establish a pattern for this type of question.