Question 890517


the log equation is equivalent to the exponential equation as defined by the identity equation shown below:


logb(a) = y if and only if b^y = a


this statement reads:


log of a to the base of b is equal to y if and only if the base of b raised to the power of y is equal to a.


this works for any base, including the base of e which is what LN represents.


ln(x + 9) = loge(x + 9)


e is the scientific constant of 2.718281828...


this statement says that the natural log of (x + 9) is equal to the log of (x + 9) to the base of e.


your equation of ln(x + 9) is equivalent to loge(x + 9).


the log identity formula applied to your problem is:


loge(x+9) = y if and only if e^y = x + 9


if you solve for x in this equation, you get x = e^y - 9


instead of x being the independent variable, y is the independent variable.


the graph of y = ln(x+9) is identical to the graph of x = e^y - 9.


i'll show you  that further down.


normally you choose values for x and find the equivalent value of y through the use of the formula.


here you will choose values for y and find the equivalent value of x through the use of the formula.


then you graph the coordinate points that you have.


create a table with values for y from y = -4 to + 4 and calculate x = e^y - 9 for each value of y.


your table will look like this:


<pre>

y     x

-4    -8.98
-3    -8.95
-2    -8.87
-1    -8.63
 0    -8.00
 1    -6.28
 2    -1.61
 3     11.09
 4     45.60

</pre>


you are looking for the value of y and then finding the corresponding value of x.


the graph of your equation of x = e^y - 9 will look like this:


<img src = "http://theo.x10hosting.com/2014/080106.jpg" alt="$$$" </>


this is identical to the grah of y = ln(x+9) that is shown below:


<img src = "http://theo.x10hosting.com/2014/080107.jpg" alt="$$$" </>