(187)273 X (456)135 X (299)424 X (588)139 X (394)154 X (181)177 X
(1342)437 = .....x

This is a sum from Indices.
That would be 187 raised to the power 273 and likewise for the other
numbers... the superscript didn't show up.

There's got to be a shortcut method to solve this. I just can't see
it. Pleeeeeeeeeease Help!!! I need this at the earliest by thursday.

Thankyou sooo much.

2. Originally Posted by cogscineuro
(187)273 X (456)135 X (299)424 X (588)139 X (394)154 X (181)177 X
(1342)437 = .....x

This is a sum from Indices.
That would be 187 raised to the power 273 and likewise for the other
numbers... the superscript didn't show up.

There's got to be a shortcut method to solve this. I just can't see
it. Pleeeeeeeeeease Help!!! I need this at the earliest by thursday.

Thankyou sooo much.
Logs! (in what follows log denotes the common log, that is base 10)

log(187^273 x 456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437) =
.........273 log(187) + 135 log(456) + 424 log(299) + 139 log(588) + 154 log(394) + 177 log(181) + 437 log(1342)~=4579.9444

So the product ~=8.799 x 10^4579

RonL

3. Originally Posted by CaptainBlack
Logs! (in what follows log denotes the common log, that is base 10)

log(187^273 x 456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437) =
.........273 log(187) + 135 log(456) + 424 log(299) + 139 log(588) + 154 log(394) + 177 log(181) + 437 log(1342)~=4579.9444

So the product ~=8.799 x 10^4579

RonL
This, by the way, is how your calculator does the problem.

-Dan

4. Originally Posted by topsquark
This, by the way, is how your calculator does the problem.

-Dan
My calculator (if I could find where the children have put any of them)
wouldn't, it/they cant display a number with a four digit decimal exponent!

RonL

5. Originally Posted by CaptainBlack
Logs! (in what follows log denotes the common log, that is base 10)

log(187^273 x 456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437) =
.........273 log(187) + 135 log(456) + 424 log(299) + 139 log(588) + 154 log(394) + 177 log(181) + 437 log(1342)~=4579.9444

So the product ~=8.799 x 10^4579

RonL
In order to understand what is going on here you need to know
some of the laws of logarithms.

1. log(A*B)=log(A) + log(B)

2. log(A^x)=x log(A)

Applying law 1 we have:

log(187^273 x 456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437)
...........= log(187^273) + log(456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437)
...........= log(187^273) + log(456^135) + log( 299^424 x 588^139 x 394^154 x 181^177 x 1342^437)

and so on to get:

log(187^273 x 456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437)
...........= log(187^273) + log(456^135) + log(299^424) + log(588^139) + log(394^154) + log(181^177) + log(1342^437).

Now apply law 2 to each term on the righthand side of the "=" sign
to get the result given earlier:

log(187^273 x 456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437) =
.........273 log(187) + 135 log(456) + 424 log(299) + 139 log(588) + 154 log(394) + 177 log(181) + 437 log(1342).

Now this can be evaluated on a calculator, to (if I have done this right) 4579.9444.

But by the definition of common logarithms if log(a)=b, then
10^b=a. Now we have:

log(187^273 x 456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437) = 4579.9444,

so:

187^273 x 456^135 x 299^424 x 588^139 x 394^154 x 181^177 x 1342^437
.........~= 10^4579.9444 = 10^4579 x 10^0.9444
.........~= 8.799 x 10^4579.

RonL