Question

( 4 * 9 ^ x ) - ( 7 * 12 ^ x ) - ( 3 * 16 ^ x ) = 0

Answer 1

Sorry its ( 4 * 9 ^ x ) - ( 7 * 12 ^ x ) + ( 3 * 16 ^ x ) = 0

Answer 2

You can check that x =0 is a solution.

Answer 3

and x=1

Answer 4

Also x=1

Answer 5

I was searching for something like more precise.
For example we have 4 * 3 ^ 2x - 7 * 4 ^ x * 3 ^ x + 3 * 4 ^ 2x = 0 and if we replace 3 ^ x with i and 4 ^ x with j we come to this:
4 * ( i ^ 2 ) - 7 * i * j + 3 * j ^ 2 = 0 and then...

Answer 6

\[
4\ 9^x-7\ 12^x+3\
16^x=\left(4\ 3^x-3\
4^x\right)
\left(3^x-4^x\right)=0
\]

Answer 7

x=0 and x=1 are the only solutions. Look at
http://www.wolframalpha.com/input/?i=plot+4+9^x+-+7+12^x+%2B+3+16^x+from+x+%3D-2+to+1.2