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This one was confusing me a bit.

ln (x)² = 2ln(x)

but with 2ln(x) x must be >0

and with ln (x)²  x is just in the set of reals.

How does that work???

Ahhhhhhhh! THOSE SMILEYS THO!!!!!!!

Melody's first answer is correct....here's a graph of the solution....

As for the second question, we have........ log₅(2x-1) = 2.........in exponential form, we have

5² = 2x-1

25 = 2x -1     subtract 1 from both sides

26 = 2x         divide by 2

13 = x

And there you go......

Hey chris isn't this 62.51 because i did 3.44% of 1,817.43 and got that.... i hope its right?

zegroes answer is good.......if we wanted to express it as a fraction, note that we could cancel the "5" with the "10" before we multiplied, giving us

(1/4) * (9/2) = 9/8   (which = 1.125, just as zegroes said !!!)

989.88518149.How i got this was do 5 gallons=18.9270589  liters then do 2 quarts=1.89270589 liters   then do 6 gallons=22.7124707 liters   then finally do 1 quarts=946.352946 liters   add em all up then you get your answer

Good job, Melody......you're exactly correct with the nultiplication........

Note that it is easy to remember how to find a paricular element in matrix multiplication. To find element a_ij in the resultant matrix, we just multiply the "ith" row of the first matrix times the "jth" column of the second!!

1.12500 

I'm not great at these kinds of problems, but I always like to give 'em a try!!!.........

Let A be the probabilty of one side showing "red".......and let B be the probabilty that both sides are red.

We already know that the double-sided white card doesn't matter, since we already have a card showing "red."

So we have

(Probability of Two sides Red l One side is Red) = P(A and B) /  P(A)

P(BlA) = [(1/2) * (1/2)] / (1/2)  =    (1/2)

Another way of looking at this is that we either have the double-sided red card, or we don't !!!

That's my two cents worth, anyway !!!

Are you paying off a loan or is the money sitting in the bank earning interest?  Is interest paid/given monthy or yearly or what.

Now Paulina - you have to respond by hitting the post answer button.

1) ln (4-x) + ln(2) = 2 ln(x)

$$\begin{array}{rll}
ln(2(4-x))&=&ln(x^2)\\\\
8-2x&=&x^2\\\\
x^2+2x-8&=&0\\\\
(x+4)(x-2)&=&0\\\\
x=-4\qquad &or& \qquad x=2
\end{array}$$

now I am confused as well.

You cannot have  the ln of a negative number so I guess x=2

Thanks for the help! Appreciate it Melody! 

Thanks for the thumbs up 

$$\[ \left( \begin{array}{cc}
1 & 2 \\
3 & 4
\end{array} \right)
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)
\]
\[ \left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)+
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 12 \\
1 & 18
\end{array} \right)
\]$$

\[ \left( \begin{array}{cc}
1 & 2 \\
3 & 4
\end{array} \right)
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)
\]
\[ \left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)+
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 12 \\
1 & 18
\end{array} \right)
\]

$$\[ \left( \begin{array}{cc}
1 & 2 \\
3 & 4
\end{array} \right)
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)
\]
\[ \left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)+
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 12 \\
1 & 18
\end{array} \right)
\]$$

I've never done that before - I'm quite pleased with myself!

i do it like

AB11= 1X2, 2X-1 = 0

AB12= 1X6, 2X0  = 6

AB21= 3X2, 4X-1 = 2

AB22=-3X6 4X0 = 18

So im just wondering if i put it   0(AB11)   2(AB21)

                                              6(AB12)   18(AB22)

Hang on I'm trying to work out how to do matrix input.    Ummm

so would that be..

AB= 0 2     +   B= 2 6

      6 18              -1 0

You just add the ones that are in the same position.

sin45=1/(sqrt2)

sine 90=1

When x is on the bottom it is easiest just to take the reciprocal of both sides

$$\frac{45}{sin45}=\frac{x}{sin90}\\\\
45\sqrt2=x\\\\
x=45\sqrt2$$

I believe that the answer is a half because the other side has to be either white or red.

the fact that it is red on one side is a given so the all white card has got nothing to do with it.

I guess that we do too.  thanks Rosala lol.

$$97000=71127e^{0.073t}\\\\
\frac{97000}{71127}=e^{0.073t}\\\\
ln\left(\frac{97000}{71127}\right)=ln e^{0.073t}\\\\
ln\left(\frac{97000}{71127}\right)=0.073t(lne)\\\\
ln\left(\frac{97000}{71127}\right)=0.073t\\\\$$

You should be able to finish it.  If you want me to check your answer I can to that. 

Thanks NinjaDevo,

This looks great.

I've decided that this needs to go into the Sticky Notes (to replace the other one)

If it is not there no-one will use it and that defeats the whole purpose.

I will comment on it as I use it.

Please, NinjaDevo and I want your feed back.

Please use this information thread and add any relevant comments.

People are welcome to add their own reference / comment page BUT

Please just use one post as your own and edit it when needed.