Can you solve this in 10 seconds

Algebra Level 2

$(\log_{10}100)(\log_{10}99)(\log_{10}98)(\log_{10}97) \cdot \cdot \cdot (\log_{10}(-100)) = \ ?$

0 None of these choices -1 1

12 solutions

Paul Ryan Longhas
Apr 10, 2015

$(\log_{10}100)(\log_{10}99)(\log_{10}98)(\log_{10}97)..............(\log_{10}0)........$

But $\log_{10}0$ is not defined

Try this one

Moderator note:

Yes correct. Note that a common mistake students make is to consider Zero Product Property without checking that all the terms (being multiplied) are defined and finite.

You should give the termination term. One can assume that it ended on x=1.

Prakash Chandra Rai - 6 years, 2 months ago

Even i thought the same

Rohit Ner - 6 years, 2 months ago

when i solved this problem worth 210 points

Prakash Chandra Rai - 6 years, 2 months ago

I agree. It would clarify the problem more.

Akshay Manjarekar - 6 years, 1 month ago

In the problem, it was given until log(-100), How can you assume

Prateek Singh - 6 years, 1 month ago

this question is modified . Question was different when I solved.

Prakash Chandra Rai - 5 years, 10 months ago

The termination term is given -100. So for any negative number the logarithm is undefined.

Jigar Sheth - 6 years, 1 month ago

log(-1)=iπ/ln(10)

Matthew Musick - 6 years, 1 month ago

I forget log10(0) is undefined I thought that log10(1)=0 and hence all the term become zero

Muhammad Abdullah Tariq - 6 years, 1 month ago

The logarithm of a negative number is complex but log(0) is in fact undefined. Without that term in product would be zero.

Amy Waldhauer - 5 years, 4 months ago

I too assumed it to end at x=1 and therefore got 0 as the answer

Rishabh saraswat - 6 years, 2 months ago

Even i did the same..

Nithin Nithu - 6 years, 2 months ago

Undefined x 0 is undefined.

Anelize Theron van Biljon - 5 years, 10 months ago

I don't think it depends on finite terms. Anything multiplied by ZERO (0) gives zero no matter what. CORRECT ME IF I M WRONG.

Shafi Ahmed - 6 years, 1 month ago

yes, but log(0) is undefined

Benedict Almeda - 5 years, 10 months ago

Diego Armando Pulido Ramos
Apr 18, 2015

Log of negative numbers doesn't have sense in Real Numbers

Hitesh Abichandani
Jun 9, 2015

Log of zero, and negative quantities is not defined,

Sameer Marathe
May 11, 2015

Log0 isn't defined as well as logarithm of negative numbers its simply goes to complex number so real number shouldn't be answer

Arvindh Balasubramani
Apr 19, 2015

Log doesn't meant for negative numbers .

Martin Kok
Apr 20, 2015

log base 10 to negative 100 is undefined, therefore the answer would not be a whole number, therefore none of those choices fit the criteria as a right answer.

Kevin Silva
Apr 19, 2015

Log base(x) y = z Where y>0

Brian Lee
Apr 20, 2015

Anything past log 1 is undefined. You cannot have a log of a negative number of of zero.

Nabil Azmi
Apr 20, 2015

log1=0 , log 0 undefined , thereis no log negative numbers so the answer is undefined

Yasasweni Balaji
Apr 19, 2015

Logarithm of zero and negative numbers are not defined, i guess, hence there cant be a definite answer it

Brent DeJong
Apr 19, 2015

log is not defined for any negative numbers, unless we allow complex solutions. Even then, log(0) is not defined.

Satyabrata Biswas
Apr 18, 2015

only by inspection the alternative selected was found to be rational.

Can you solve this in 10 seconds

12 solutions

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