Question 1007427
normally, when x is in the exponent, you would solve using logs.


you would take the log of both sides of the equation to get:


3^x = 9x becomes:


log(3^x) = log(9x) which becomes:


x * log(3) = log(9x)


solve for x and you get:


x = log(9x) / log(3)


it does not appear that there is a way to isolate x to one side of the equation.


if there is a way, i don't know it.


i usually solve these types of problems by graphing.


start with 3^x = 9x


subtract 9x from both sides of this eqaution to get 3^x - 9x = 0


you would graph y = 3^x - 9x and look for the zero crossing points.


those would be the common solutions.


doing it this way is the same as graphing y = 3^x and y = 9x and looking for the intersection points.


both methods would get you the same value of x.


the graph of y = 3^x - 9x is shown below:


<img src = "http://theo.x10hosting.com/2015/120202.jpg" alt="$$$" </>


you can see that the zero crossing points are at x = .128 and x = 3.


those are rounded values.


a graphing calculator such as the TI-86 plus will give you more decimal places in the result.


that calculator would tell you that the zero crossing points are at:


x = .12786942 and at x = 3


if you look at each equation individually, you will find that:


y = 3^x = 1.150824821 when x = .1278694246 and y = 9x = the same.


y = 3^x = 27 when x = 3 and y = 9x = the same.


i have yet to figure out how to do this algebraically, but if you have a good graphing calculator, you should always be able to find the solutuion graphically as long as the values are real.