geno3141

If the variable is in the exponent, use logs:

2^(3x - 4)  =  5

log[ 2^(3x - 4) ]  =  log(5)

The reason for using logs: the exponent comes out as a multiplier:

(3x-4)·log(2)  =  log(5)

Divide by log(2);

   3x - 4  =  log(5) / log(2)

   3x  =   log(5) / log(2) + 4

     x  =  ( log(5) / log(2) + 4) / 3

Just like  π  has been defined to be  3.1415926..., 

i  has been defined to be  √-1  and so  i²  is  -1.

In both cases one symbol has been used to replace a more complex expression.

I would suggest trying it over, but change your x-values to  8, 9, 10, 11.

Le x represent item A; let y represent item B.

x + y ≥ 10     10x + 30y ≤ 200

To graph  x + y ≥ 10  by plotting points:

  If x = 0, y = 10   --->  (0, 10)                              If y = 0, x = 10     --->     (10,0)

  Plot the two points,  (0, 10)  and  (10, 0); draw the line that connects them; shade above the line (because of the ≥ sign).

To graph  10x + 30y ≤ 200  by plotting points

  If x = 0, y = 20/3     --->     (0, 6 2/3)              If y = 0, x = 20    --->     (20,0)

  Plot the two points; draw the line that connects them; shade below the line (because of the ≤ sign).

I'm not sure that this will answer your question, because this will find the final value (which is not usually called an annuity); this will find the value of $200 invested at 9%, compounded annually, for 9 years.

The final value is found by using this formula:  A  =  P(1 + r/n)^(n·t)

A  =  final amount                  P = inital payment = $200.00        r = rate (as a decimal) = .09

n = number of times compounded per year = 1                            t = number of years = 9

A = 200(1 + .09/1)^(1·9)    $434.38

If the problem is:       √x  =  0.9,

square both sides:  (√x)²  =  (0.9)²

                                  x  =  0.81

Rewrite them from ighest exponent to lowest:

    -g³ +3g² + 4g - 2

If  y  =  ln(3x) - 1.

There are two steps to find the inverse:

1)  Exchange x and y:

     x  =  ln(3y) - 1

2)  Solve for y:

     x + 1  =  ln(3y)

     e^(x + 1)  =  e^(ln(3y))

     e^(x + 1)  =  3y

     y  =  (1/3)e^(x + 1)

Speed is the distance divided by the time.

To get velocity, first find the speed and then also attach the direction. 

What is the question?