CPhill

A log is just an exponent (power), rosala..let me demostrate....

For example  log₂ (8)   says this....what power (exponent) do we put on "2" (called the base) to raise this to 8 ?? The answer is "3.'   This is because 2³ = 8  !!!

The most common bases are 10 and "e"  (e ≈ 2.718)  ...Normally, the base 10 log is notated without the base - the base is understood to be 10 - and the base "e" log is notated as "ln"  ......called the "natural log".......the natural log base is extremely useful in many scientific applications.  So base 10 log  of 100 would be notated as  log(100) and the natural log of 100 would be notated as ln(100).

(Note.....We can actually use any positive number - except 1 - as a base!!!)

Very nice, rosala.......this is exactly what Melody was referring to......we should be telling them HOW to get the answer instead of working the WHOLE problem......!!!

I should do this more, myself !!!

Assuming that we have   log(4) + log(32)  we have

log(4 * 32) = 

log (128)

Remember what this says...it says that the cosine of some angle = 1 ..  and where does that happen???  When the angle = 0 ..... and, of course, every multiple of 360° after this......

That's it !!

So we have, using a property of logs.....

log(3/x) + log(x^2) + log(3x)^3 =

log(3/x) + log(x^2) + log (27x^3)     .....and by another property pf logs, we have

log((3/x)*(x^2)*(27x^3)) =

log (81x^4)

We could also write this as log(3x)^4 = 4 log(3x)

Let's call the number that went to the hall "x".....then the number that went to the stadium is just "20-x"

And the number that went to the hall times the price of a hall ticket plus the number who went to the stadium times the price of a stagium tickest = $750. Mathematically, we have...

(x)(30) + (20-x)(60) = 750     simplify this.......

30x + 1200 - 60x  = 750

-30x = -450    divide both sides by -30

x = 15    and this is the number who went to the hall

And (20-x)  = (20-15) = 5......and that's the number who went to the stadium

Let's multiply through by -1 to get rid of all those nasty negatives !!.....so we have

7/(x+1) = 8 + 5/(x - 2)   ....and getting a common denominator on the right , we have....

7/(x+1) = [8(x-2) + 5]/(x-2)  ..... simplify on the right

7 /( x+1) = (8x - 16 + 5) / (x-2)

7 / (x+1) = (8x - 11) /(x -2)   .....one way to solve this is just to cross-multiply

7(x-2) = (x+1)(8x-11)

7x - 14 = 8x^2 - 3x - 11  ......subtract 7x and add 14 to both sides

0 = 8x^2 - 10x + 3      ......see if this factors

(2x - 1)(4x - 3) = 0

And setting each factor to 0, we have that x = 1/2 or x = 3/4

Loved the humorous pics, rosala....and I agree......what's the point of making posters if no one can SEE THEM???......what a waste of time...!!!!

If Melody and I don't start answering more questions, we might get "passsed" one day !!!.....I think you young guys are just too fast for us !!!!

To get an idea of how large a "googol" is, let's suppose that we could write out one billion zeroes per second.

Now, one billion seconds is about 31.7 years......and let's suppose that we lived for three billion seconds, or about 95 years. And let's suppose that we started writing our zeroes at birth and never took a break for our entire lifetime !!!

Then the number of zeroes that we could write is  (3 x 10⁹ x 10⁹ ) = (3 x 10¹⁸)

So the number of "lifetimes"  that would be required for us to complete the job is, approximately............ (10¹⁰⁰ ) / [3 x 10¹⁸ ] = about  [3.33 x 10⁸²] "lifetimes"