Question 47776
3^x+5 = 9^x

9^x-3^x-5=0
(3^x)^(2) - 3^x -5 = 0

This is a quadratic where the variable is 3^x
Let 3^x = w, then rewrite the problem as:
w^2 - w -5 =0
Use the quadratic formula to get the following:
w=[1+-sqrt(1+20)]/2
w=[1+-sqrt(21)]/2

Now, reverting back to the fact that w=3^x you get:
3^x=[1+-sqrt(21)]/2
3^x=2.79128785... or 3^x is a negative number( which it cannot be)
Take the log to get:
xlog3 =2.79128785...
The x=5.85026934...
Cheers,
Stan H.