All Answers 358516 Answers

Ah, yes...I mis-read it...the correct answer should be..... 12 ( a + c) + 13 b

log 5 = a     log 3 = b   log 2 = c    find log₃₀ 8

Note :  log 5 + log 3 + log 2   = a + b + c     and we can write

log (5 * 3) + log 2  = a + b + c

log15 + log 2  = a + b + c

log (15 * 2)  = a + b + c

log (30) = a + b + c 

And note, using the change of base rule ...  log₃₀ 8  =  log8 / log 30 ......so....

log₃₀ 8  =  log8 / log 30  = log 8 / [ a + b + c ] =    log 8 / [ log 5 + log 3 + log 2]  ≈ .611 

CPhill: The middle term is "13b", or do you think that is a typo.

Thanks...but after that one....maybe I should have used a "crutch".....LOL!!!!!

 12*c+13*b+12*a   factor the 12 out of each term

12 ( c + b + a)      and that's all we can do.....

CPhill: Congrats. simply brilliant that would get the same result, manually, as Alan did using computer software!!. Look at W/A result and see if you can make any sense of it.

-(6x-2) = 2(x-2)   distribute the negative outside the parentheses on the left

-6x + 2 = 2x - 4     add 4, 6x to each side

6 = 8x     divide both sides by 8

6/8 =  x   = 3/4

log _a+b m  + log _a-b m -2log_a+b m*log_a-b m     if m^2 = a^2 - b^2  .....

If m^2 = a^2 - b^2  then   m^2 = (a -b)(a + b) → m = √[ (a - b)(a + b)]  ...[we assume that m is positive]...so we have

log _a+b √[ (a -b)(a + b)]   + log _a-b √[ (a -b)(a + b)]  -2log_a+b √[ (a -b)(a + b)] *log_a-b √[ (a -b)(a + b)] =

log _a+b √(a + b) + log _a+b √(a - b) +  log _a-b √ (a - b) +  log _a-b √(a + b)

- 2[log_a+b√(a -b) + log_a+b √(a +b)] [log_a-b √ (a -b) + log_a-b √(a + b) ]  =

1/2 +  log _a+b √(a - b)  +1/2 + log _a-b √(a + b) - 2 [ log_a+b√(a -b) + 1/2] [ 1/2 + log_a-b √(a + b) ]  =

1 + log _a+b √(a - b) + log _a-b √(a + b) - 2[ 1/4 + (1/2)log_a-b √(a + b) + (1/2) log_a+b√(a -b) +  log_a+b√(a -b)log_a-b √(a + b)]  =

1 + log _a+b √(a - b) + log _a-b √(a + b) - (1/2) - log_a-b √(a + b) - log_a+b√(a -b) -2 log_a+b√(a -b)log_a-b √(a + b)  =

1/2 + log _a+b √(a - b) +  log _a-b √(a + b) - log_a-b √(a + b) - log_a+b√(a -b) - 2 log_a+b√(a -b)log_a-b √(a + b)  =

1/2 - 2 log_a+b√(a -b)log_a-b √(a + b)  

1/2 - 2 [(1/2) log_a+b (a - b) (1/2)log_a-b (a + b) ]  =

1/2 - 2[1/4] [ log_a+b (a + b) * log_a-b (a + b)]  =    use the change of base rule in the brackets

1/2 - (1/2) [ (log (a - b) /log (a + b)] [ log(a + b) / log (a- b) ] =

1/2  - (1/2) [ log(a -b)/log(a -b)] [ log (a + b)/log (a + b) ]  =

1/2 - 1/2 * [ 1] * [1 ]  =

1/2 - 1/2  =

0

LOL!!!!....mine was even more complicated than Alan's  !!!!!!!

Alan: Look at W/A here and see if it makes any sense! It is simply beyond me! :

http://www.wolframalpha.com/input/?i=m%5E2%3Da%5E2-b%5E2,+Logbase(a%2Bb)(m)%2BLogbase(a-b)(m)-2Logbase(a%2Bb)(m)*Logbase(a-b)(m)

\(-2\frac{1}{4}+\frac{4}{5}\rightarrow-\frac{9}{4}+\frac{4}{5}\rightarrow-\frac{45}{20}+\frac{16}{20}\rightarrow-\frac{29}{20}\rightarrow=-1\frac{9}{20}\)

.

I don't know how to enter it in Wolfram Alpha either!  

The symbolic math in Mathcad gives 0 as the result.  Unfortunately, it doesn't show how it works it out.

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I should note that an assumption in the above is that a is greater than b.

In a class of 32,  5/8 are girls. How many boys are there?

1 - 5/8 =3/8 must be boys

3/8 x 32 =12 are boys

5/8 x 32 =20 are girls

Alan: If you feel there is a simpler way, God help the rest of us!!. Can you try Wolfram/Alpha and see what they come up with. I don't even know HOW to enter it!.

Like so:

I've a feeling there must be a simpler way!!

Don't really understand this one!! CPhill to the rescue!.

a = (8 log(30))/(log(5)), b = (8 log(30))/(log(3)), c = (8 log(30))/(log(2)), x = 656,100,000,000

960 - 170 =790 Net capacity of the elevator with his weight included.

790 / 40 = 19.75 or rounded to 19 boxes that he can take up in one trip.

-4.45

Previous post by "Guest" is not correct.

572^29 mod 713 = 113

Ummmm

And any isotopes of iron.

*showing off my chemistry skills although I just started chemistry lessons this year*

26 protons means its atomic number is 26. That means it is iron :).

*Pikachu isn't using iron tail.*

This site is where people get help for their homeworks(better not throw all your homework on here.), daily calculations, maths for sciences, literally maths for everything :)

Hope this helps :):)

I will give my own definition with my understandings.......

Life, is that when you can't be omniscience, when you can't be omnicompetent, when you can't be perfect. Life is when you are physically and mentally existing, when you try to have your physical body and your mind linked, when you try to get a new life.

A simpler version:(I think that's a bit different )

Life:

1. You CANNOT be perfect in life.

2. You try your best in your life.

3. You are forced to cherish your life.

It takes me some time to write these sentences. I checked 'omnicompetent' up because I have this word in mind but I don't remember what is its meaning. I hope this will help you.