# Log and sqrt ? HELP !

#### dentalstd2008

##### dental student to be
10+ Year Member
Hey guys,
Does anyone know how to calculate Log and Square Root ( complicate number) WITHOUT A CALCULATOR ? I mean, is there any formular ?
For example:
How to CALCULATE square root of 1x10^-5 ?
How to CALCULATE -log(3.2x10^-3) ?
I appreciate your help a lots !!

#### Ron Jeremy

10+ Year Member
The answer of 1*10^-5 is just 0.00001 because this is equal to 1*(1/100,000) = 1*(0.00001). Basically, take 1 and just move the decimal place over 5 places to the left. This type of problem WILL BE on the DAT. With practice, you should be able to answer this type of problem in 10 sec.

I have no idea why you would ever need to figure out -log(3.2X10^-3) without a calculator. This WILL not be on the DAT. The QR section is all about finding ways to make straightforward calcualations that tests your ability to know/see opportunities of cancellations and math identities. Where did you get this -log question?

#### toothgirl86

10+ Year Member
To find the log of a number, there's a trick that kaplan teaches.
For example, if you want to find log 3.5 * 10^6, calculate it like this:
6 - log 3.5... you can estimate this to be around 5.7
Basically you take the exponent and make that the first number, then you take the first number and you have to estimate the log of it and find the difference. The answer choices for this type of problem will usually be really different, so it will be easy to tell which answer is the right one.
Hope this helps!!

#### Ron Jeremy

10+ Year Member
Toothgirl's method for log problem is right. The real answer for the -log(3.2*10^-3) is 2.5. Using toothgirl's approximation would give 3-3.2 = 2.68 which is close to 2.5. Maybe this will be on the DAT.

See, you learn little math tricks everyday #### DDSurfer

##### Cheeeeeze
10+ Year Member
Toothgirl's method for log problem is right. The real answer for the -log(3.2*10^-3) is 2.5. Using toothgirl's approximation would give 3-3.2 = 2.68 which is close to 2.5. Maybe this will be on the DAT.

See, you learn little math tricks everyday I wish it was just as easy as seeing it here and learning it #### Streetwolf

##### Ultra Senior Member
10+ Year Member
7+ Year Member
The answer of 1*10^-5 is just 0.00001 because this is equal to 1*(1/100,000) = 1*(0.00001). Basically, take 1 and just move the decimal place over 5 places to the left. This type of problem WILL BE on the DAT. With practice, you should be able to answer this type of problem in 10 sec.
No the OP asked for the square root of 1x10^-5 (AKA just 10^-5).

That would be the sqrt(1/10^5) which is the same as sqrt(1/10^4)*sqrt(1/10).

So the first one is just 1/10^2 = 1/100.
The second one is trickier. The square root of 10 is approximately 3.15 or so. So I would say 1/3.15 * 1/100 = 1/315. That's approximately 0.00317 with long division.

Actual answer is ~ 0.0031623 so we're right on the money.

#### Ron Jeremy

10+ Year Member
Streetwolf is totally right. I totally misread the question. I knew I should have just went to bed instead of trying to figure out a math question after studying three exams.

#### z3u2

10+ Year Member
To find the log of a number, there's a trick that kaplan teaches.
For example, if you want to find log 3.5 * 10^6, calculate it like this:
6 - log 3.5... you can estimate this to be around 5.7
Basically you take the exponent and make that the first number, then you take the first number and you have to estimate the log of it and find the difference. The answer choices for this type of problem will usually be really different, so it will be easy to tell which answer is the right one.
Hope this helps!!
actually...
log (3.5*10^6)
= log (3.5) + log(10^6)
= log (3.5) + 6
~= 6.3

to the OP:
review some basic log rule
like log (AB), log(A/B) and log(A^B), and understand what log means will help.