9^2x = 3^x+6 x+6-6=0
x+6 -6 you subtract 6 which is why I thought the answer was -6 since 0 wasn't right.
9^2x= 3^4x
3^4x= 3^(x+6)
4x = x + 6 solve for x.
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To solve the equation 9^(2x) = 3^(x+6), you need to rewrite both sides of the equation with the same base. Since both sides have a base of 3 raised to some power, we can rewrite 9 as 3^2.
9^(2x) can be written as (3^2)^(2x), which simplifies to 3^(4x).
So, the equation becomes: 3^(4x) = 3^(x+6).
Now that both sides have the same base, we can equate the exponents:
4x = x + 6.
To solve for x, you need to isolate it on one side of the equation. You can do this by subtracting x from both sides:
4x - x = 6.
This simplifies to:
3x = 6.
Finally, divide both sides of the equation by 3 to solve for x:
x = 6/3.
x = 2.
Therefore, the solution to the equation 9^(2x) = 3^(x+6) is x = 2.
If you need further assistance or would like to improve your math skills, seeking a tutor can be a helpful resource. A tutor can provide personalized guidance and help you understand the concepts you are struggling with.