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:
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.
