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Here's another approach....using Alan's interpretation

log₂x = log₄(4x)

log₂x  = log₄4  + log₄x

log₂x - log₄x  = log₄4

log₂x - log₄x  = 1

logx/log2  - logx/log 4   = 1

logx [ log4 - log 2] / [log2 * log 4]  = 1

logx  = [log2 * log4] / [ log4 - log2]

logx = [log2 * log4] / [log (4/2)]

logx = [log2 * log4] / [log2]

log x  = log 4

x = 4

Suppose you have a 15-year loan for $355,000 with an APR of 3.75%. Using your calculator or Excel, make a table showing the amount of interest paid, the amount of principal paid, and the ending balance for each of the first 3 months of the loan. Be sure to report only your Month 3 results.

We have to assume that 3.75% is compounded monthly.

Then we to calculate the blended monthly payment, which comes to=$2,581.64

AMORTIZATION SCHEDULE:

Principal                   Interest                  Balance

1-$1,472.26              $1,109.38                $353,527.74

2-$1,476.87              $1,104.77                $352,050.87

3-$1,481.48              $1,100.16                $350,569.39

I assume you want to know what point the two equations intersect so I will show that through algebra.

\(y=9.65x+43\)

\(y=8.40x+58\) or \(y=8.4x+58\)

\(9.65x+43=8.4x+58\)

\(9.65x=8.4x+15\)

\(1.25x=15\)

\(x=12\)

\(y=8.4(12)+58\)

\(y=100.8+58\)

\(y=158.8\)

The point that these two equations go through is the ordered pair \((12, 158.8)\)

Here is the graph showing the two eqations and the ordered pair they both go through\

Here's another way to see this.......2 men are just 2/3rds the labor of 3 men.....therefore....it should take them 3/2 times as long to do the job.....so....

3/2  * 20    =  30 minutes

y=9.65x+43    y=8.40x+58

Let's just set the equations equal

9.65x + 43  = 8.40x + 58      subtract 8.40x, 43 from both sides

1.25x  = 15      divide both sides by 1.25

x = 12

And we can use the first equation to find y

y = 9.65(12) + 43  =   

      115.8  +  43   =

       158.8

So....the solution is  {x , y}   = { 12, 158.8}

The solutions to x² - 8x  =  24:

First, get all terms to one side by subtracting 24 from both sides:

                         x² - 8x - 24  =  0

Now, try factoring this  --  but it doesn't factor nicely  -- so you can graph this, use the quadratic formula or complete the square -- I'm choosing to complete the square.

Back to moving the number back to the right side:

                        x² - 8x  =  24

Since the coefficient of the x-squared term is 1, work with the coefficient of the x-term --  -8

Completing the square is a three step process:

     --  first, divide the coefficient of the x-term by 2:  -8 / 2  =  -4

     --  second, square this number:  (-4)²  =  16

     --  third, add this number to both sides of the problem:

                  x² - 8x + 16  =  24 + 16

Factor the left side, simplify the right side:

                  (x - 4)(x - 4)  =  40

                          (x - 4)²  =  40

Take the square root of both sides:

          either  x - 4  =  sqrt(40)     or  x - 4 = - sqrt(40)

so      either  x  =  4 + sqrt(40)     or  x  =  4 - sqrt(40)

solve for x:
x^2-8 x=24

Add 16 to both sides:
x^2-8 x+16=40

Write the left hand side as a square:
(x-4)^2=40

Take the square root of both sides:
x-4=2 sqrt(10) or x-4=-2 sqrt(10)

Add 4 to both sides:
x=4+2 sqrt(10) or x-4=-2 sqrt(10)

Add 4 to both sides:
Answer: |  x=4+2 sqrt(10)       or       x=4-2 sqrt(10)

A basketball player attempted 24 shots and made 13. If this percentage continues, the probability that the player will make the next shot is 13/24 for a probability of (about) 0.542.

Since each person is doubling the number of people, 1 finds 2 more, and 2 find 4 more....etc., then this becomes an exponential growth, which grows like this: 1, 2, 4, 8, 16....., or:

1 x 2^48=281,474,976,710,656 dollars in 48 hours. But, this is only theoretical, because there are only 7.3 billion people in the world!. For 7.3 billion people, you would only need:Log(7.3 x 10^9) / Log(2) =~33 doublings.

3 men can unload a van in 20 minutes. how long it takes to do the same job with two men?\

{Google Translator}

If 3 men can unload a van in 20 minutes, then it means that 3 men can finish 1/20 of the job in 1 minute. Or 1 man can finish the job in: 3 x 20 =60 minutes.
So, if one man can finish 1/60 of the job in 1 minute, then 2 men can finish 2 x 1/60=1/30 of the job in 1 minute. Therefore, 2 men can unload the van in 30 minutes.

you put 25,000 in the bank. then you pay 300 a month at an interest rate of 5% for 10 years. how much will you have in yyour account 10 years later? how much youve in earned in intrest alone? how much total from you actual deposits?

Will assume that 5% is compounded monthly, then after 10 year you will have accumulated=$87,759.92-Principal plus interest.

$87,759.92 - $25,000 - [$300 x 120] =$26,759.92 Interest earned over 10 years.

Total deposits=$25,000 + [$300 x 120] =$61,000 over 10 years.

The formula you use to calculate is this:

-P*[(1-(1+R/100)^-N)/(R/100)]+FV*(1+(R/100))^-N-PV=0, solve for FV.

Where R=Interest rate per period, N=number of periods, P=periodic payment, PV=Present value, FV=Future value.
 

Solve for x:
2 x^2-8 x+7=0

Divide both sides by 2:
x^2-4 x+7/2=0

Subtract 7/2 from both sides:
x^2-4 x=-7/2

Add 4 to both sides:
x^2-4 x+4=1/2

Write the left hand side as a square:
(x-2)^2=1/2

Take the square root of both sides:
x-2=1/sqrt(2) or x-2=-1/sqrt(2)

Add 2 to both sides:
x=2+1/sqrt(2) or x-2=-1/sqrt(2)

Add 2 to both sides:
Answer: |  x=2+1/sqrt(2)      or          x=2-1/sqrt(2)

Youn can finish the 2nd part.

1 acre =43,560 square feet.

43,560 /2 =21,780 square feet.

You add all of the numbers up and divide the sum by how many numbers you added. If that makes sense.

SEE THIS EXAMPLE. ADD THEM ALL UP AND DIVIDE THE RESULT BY THE NUMBER OF TERMS, WHICH ARE 10 HERE:

Statistical file:
{11, 23, 24, 35, 54, 56, 76, 21, 13, 19}

Average (mean): μ=33.2
Absolute deviation: 176.4
Mean deviation: 17.64
Minimum: 11
Maximum: 76
Variance: 422.76
Standard deviation σ=20.5611283737
Corrected sample standard deviation s=21.673332308
Median: 23.5
Mode: {35, 54, 56, 76, 24, 23, 13, 19, 21, 11} - multimodal
Geometric mean: 27.5658344385
Harmonic mean: 23.183959497
Sum: 332
Sum of absolute values: 332

40/30=1.3333.........etc. - 1 =.33333........etc X 100 =33.33%

133.33333333 .........  %

Why?

40/30 cancels down to 4/3. 

'What is 4/3 as a percentage?'   just means 'how many hundredths are there in 4/3?'

How many...........           x

hundreths..........            1/100

are there  ............            =

in   4/3      .......                 4/3    

so we need to find x/100 = 4/3     for x as the percentage.

Multiply both sides by 100 to get  x = 400/3     = 133.3333333.......... which is the percentage.

Let the three digit number be n

5000 + n - 3032 = 9*n

8*n = 1968

n = 246

.

It's the same as saing 24

                                    100      

Wow!!. Thanks a million guys. I could never have been to solve it. I will study both methods carefully, and if I don't understand something, then I will seek help again.

35/100 x 55,000 =19,250 pounds.

Solve for x:
1.12165=0.153356 x

1.12165=0.153356 x is equivalent to 0.153356 x=1.12165:
0.153356 x=1.12165

Divide both sides of 0.153356 x=1.12165 by 0.153356:
(0.153356 x)/0.153356=1.12165/0.153356

0.153356/0.153356=1:
x=1.12165/0.153356

1.12165/0.153356 = 7.31408:
Answer: |  x=7.31408

I think this is meant to be:

\(\log_2x=\log_4{4x}\)

Let:

 \(a=\log_2x\\x=2^a\)

So, also:

\(a=\log_4{4x}\\4x=4^a\\x=4^{a-1}\\x=2^{2(a-1)}\)

Hence we must have:

a = 2(a - 1)   so that  a = 2, which means x = 2^a  or x = 4 

.

=26,666,666.67=26.67 x 10^6 Mbps

However, if the 0.125 in the denominator were to be 0.25 instead, then the result would be 24 Mbps.

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