it is not 19, could be 20, could be 21 but it can never be 19

15 x 3 = 45       126/4 =  31.5

So....45 - 31.5 =  13.5

And  √13.5 =  about 3.674

Very nice, Melody and Alan......I always like this type of problem!!!!

You mean the absolute value - or non directional value of it gets bigger ?

Maybe you mean

$$\\lnx=log_x(e^4)\\\\
x^{lnx}=x^{log_x(e^4)}\\\\
x^{lnx}=e^4\\\\
ln(x^{lnx})=ln{e^4}\\\\
(lnx)(lnx)=4lne\\\\
(lnx)^2=4\\\\
lnx=2\;\;or\;\;lnx=-2\\\\
x=e^2\;\;\;or\;\;\;x=\frac{1}{e^2}$$

Imagine a mass on a spring subject to Hooke's law.  

Restoring force = - k*displacement (k is positive constant)

As the displacement gets bigger the restoring force gets bigger.

.

If this is meant to be ln(x) = 4*log_x(e)  (i.e. log to base x of e) then

ln(x) = log_x(e⁴)

x^ln(x) = e⁴

Take log to base e of both sides

ln(x^ln(x)) = ln(e⁴)

ln(x)*ln(x) = 4

[ln(x)]² = 4

ln(x) = ±2

x = e² and x = e^-2

.

Thank you Alan.  I know that what you are saying is correct 

BUT 

i  find it confusing (misleading) because when teachers talk about directly proportional to they tend to say that as one gets bigger the other gets bigger but if the contant is negative this is not true.

@@ End of Day Wrap     Mon 10/11/14      Sydney,   Australia       Time 10:10 pm             ♬

Hi all,

Thanks for the thumbs up on yesterday's wrap Chris.  Much appreciated.  

It was fairly quiet today.  After all it was Sunday for many of you and it is approaching the end of the year.  In Australia schools are already winding down for the year.   

Still we had some great answers from CPhill, Alan, reinout-g, SevenUp and saseflower. A big thank you to each of you. 

Here is a few noteworthy posts:

1) Probability combinations Thanks SevenUp

Tues 11/11/14

1) Mystery log question

What is the colon for?

I have answered it - I suggest that you check youwrote it down properly 

$$\\log x = logx \times (e^4)\\$$

there is no soln to this

-------------------------------

Perhaps you mean

$$\\logx = log[x (e^4)]\\
logx = logx +log(e^4)\\$$

No - still no solutions

put

(-5)^8

onto the site calc on the home page :)

inverse trig is the same as arc trig if that is what you are after

so you use

atan, acos and asin

inverse sine is the same as arc sin

the button on the web 2 calc is labelled as asin

it is equal to 390625

$$$The range is $[1,\infty)$$

See the graph

Good one anon - I can't fault your logic :)

$${\frac{\left({\frac{{\mathtt{17\,765}}}{{\mathtt{9\,350}}}}\right)}{{\mathtt{0.015}}}} = {\frac{{\mathtt{380}}}{{\mathtt{3}}}} = {\mathtt{126.666\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

$$$The right answer is $126.\bar6$$    

42.79 is not the answer.   

You can use the symbol that Alan has shown you and this symbol is on almost all scientific calculators.

Another very common symbol for 'power of' is ^    It is above the 6 on your keyboard.

On the web 2 calc on the home page you can type what you want straight inot the input box.

so if you want (10+6)to the power of 4 you can just type in

(10+6)^4

Listen to this clip

It will be worth your while!

The general quadratic equation can be written as

y = ax² + bx + c  where a, b and c are constants.

If you are looking for the equation that gives the solutions to the quadratic equation set equal to zero, it is

$$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

.

You are right Melody, I forgot about the perimeter, so my answer for the radius should be doubled.

.