1.

`4*2^(2x)-6^x=18*3^(2x)`

Answer» `4*2^(2x) - 6^x = 18*3^(2x)`
Let `2^x = a and 3^x = b`
`=> 4a^2-ab -18b^2 = 0`
`=>4a^2-9ab+8ab-18b^2 = 0`
`=>a(4a-9b)+2b(4a-9b) = 0`
`=>(a+2b)(4a-9b) = 0`
`=> a =-2b and a = 9/4b`
When ` a= -2b`
`2^x = -2(3^x)`
`=>(2/3)^x = -2`
No, possible value for `x` with ` a= -2b`.
When `a = 9/4b`
`2^x = 9/4(3^x)`
`=>(2/3)^x = (9/4)`
`=>(2/3)^x = (2/3)^-2`
`=> x = -2`, which is the solution for this equation.


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