Math Is Fun Forum

Ricky's result in Post 9 is 2a² times as large as my result, because what he evaluates is 2a² times as large as the original question, too.

Uhh, +/- mistake corrected. Now my result is not 0 but a²/3, consistent with your result in Post 19.

This is correct instead:

hmmm.... great!

Hmm, but I like brown hair the most.

It's like tossing n dices, and to get the chance of getting the sum of dice values
less than a(sounding ei) times of the least dice value.

But it's so hard !!!!!!!!!

Next, Define S(θ)

Then

Awlsome!!

After going through so many evasive, imaginary pages of psychology, I come across some truth here!

Truth is truth- no matter how hard you try to ignore it, it will relentless show you are wrong, it is right.

Hey, guys! Sorry for the delay of the last post on powers:

First, let me explain the basics:
Shifting Bases:

Suppose you have got a table of almost all of powers of 3,
..., 3^-0.1, 3^0, 3^0.1, 3^0.2,...
Now, however, you are to calculate a power of 9 instead of 3.

9^1.5

You cannot multiply
However, you know from the table of powers of 3 that 9=3^2
Then 9= (3[sup]2[/sup])[sup]1.5[/sup]=3[sup](2*1.5)[/sup]
Find 2*1.5 and by the table you can immediately get the answer, the power of 9

So with multiplication, a table of powers of a particular number can serve to find powers of any positive number.

That's how a slide rule works to help you guage a power.
LL scale, the power tables of e, e^0.1, e^0.01, e^-1, e^-0.1, e^-0.01 calculate more than powers of the only 5 e related bases.

Now suppose you are calculate 9^1.5 by the scale of e^x and multiplication on exponetial.

Simulated Slide Rule

Use the simulated slide rule (SSR) above
Flip the SSR, find LL3+ at the bottom, e to 20M (meaning 20,000,000)
LL3+=e^D
Now you should find D[sub]1[/sub]
which satisfy
e[sup]D1[/sup]=9

D          D[sub]1[/sub]
LL3+       9

and then find D[sub]2[/sub]=1.5D[sub]1[/sub] on D scale, by multiplication of slide rule.

then you can get e^D[sub]2[/sub]=9^1.5
D        D[sub]2[/sub]
LL3+    e^D[sub]2[/sub]

Next topic is shifting LL scales, solving too large and too small problems.

However this formula almost only makes it harder to solve.
I prefer the original one.:/

Recently I came across an assertion that brush your teeth with lemon can make them whiter...