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