PCAT: Quantitative Ability Question!

[217933]

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Hey does anyone know how to solve this problem and give me the step-by-step on it? I tried looking through the Kaplan book on logarithms and they (of course) don't have anything on it even though I saw it on the PCAT like 5 times! PLEASE I NEED HELP! 😱

If Logx3 = ½ , then x =
(answer is 9 but how do you do this by hand?)

Log1,000(1/1,000) =
(answer is -1 and same thing I need to know how to do this by hand!)



And just a simple one. If there's a question asking...

What is log(2)?

How do you figure this out by hand? When I was taking Calculus we would just plug this into the calculator!

 

[Mark4275]

#1
One rule of logirthims is as followed:

A^B=C which is equal to logA(C) = B (where the A is subscripted)

Logx3 = 1/2 is equal to x^1/2 = 3

X = 9


#2
Same as #1

A^B=C which is equal to logA(C) = B

Log1000(1/1000) = X is equal to 1000^X=1/1000

X = -1


Helpful links:
http://www.sosmath.com/algebra/logs/log4/log41/log41.html
http://www.sosmath.com/algebra/logs/log4/log4.html
http://www.sosmath.com/algebra/logs/log4/log44/log44.html

 

[tprice108]

well buddy, simple but sometimes confusing concept and here i go... the first problem: Logx3= 1/2 ... you always take the little x and say "what is x if x to the 1/2 is equal to 3 (x^1/2=3) and we know when you raise something to the 1/2 power that is the same as the square root. so the answer is 9, because the square root of 9 is equal to 3.
For the second problem Log1,000(1/1000)=x ...so you say 1000 to the x is equal to 1/1000 (1000^x=1/1000) so the answer is -1.
The third is not computable by hand but you can set it up. If there is no little number, then it is assumed to be 10. so 10^x=2

 

[kismet]

And just a simple one. If there's a question asking...

What is log(2)?

How do you figure this out by hand? When I was taking Calculus we would just plug this into the calculator!

My microbio lab teacher insisted we memorize this one. I've turned my brain off cuz I graduated, so I can't tell you why it was so important, but apparently it comes up a lot. So memorize it.. log 2 = 0.301.

It might have had something to do with properties of log.. log 4 = 2 * log 2.. log 8 = 3 * log 2... log (2^x) = x * log 2. So if you memorize "log 2" you can work out several things quickly without a calculator.

We weren't allowed to have calculators on the tests and he would ask us this one anyway.. some things just have to be committed to memory.

 

[IrishRxMan]

The light at the end of the tunnel...I haven't seen nor heard of using logs in that way once you're in pharmacy school (or any other way for that matter). Besides, if you do, there's computer programs that will be doing things like that.

 

[OrllY]

log(2) is important for half life... in chemistry and math,

 

[fenixtnlfan]

Moved because of topic.