if 9^(x-12)=3^x2 find the value of x?

9^(x-12)=3^(2x)?

if so then

9^(x).9^(-12)=9^x

let p=9^x

p/9¹²=p

p=p(9¹²)

now you know what to do with your calculator am sure

let say the value for p=m/n

9^x=m/n

xlog9=(logm-logn)

z=(logan-logn)/log9

am sure your head is not cemented you should read meaning to these

9^(x-12)=3^(x^2)

3^(2x-24) = 3^(x^2)
2x-24 = x^2
x^2-2x+24 = 0
the discriminant is negative, so there are no real solutions
If you meant
9^(x-12)=3^(2x)
9^(x-12) = 9^x
x-12 = x
again, no solutions.

I suspect a typo...

is my solution step above wrong?

well, this step p=p(9¹²)

just means 1 = (9¹²)
which is false

not sure why you wandered off into the woods after that.

To find the value of x in the equation 9^(x-12) = 3^x2, we need to simplify the equation step by step.

First, we can rewrite 3^x2 as (3^x)^2 using the property of exponents.

So, the equation becomes 9^(x-12) = (3^x)^2.

Next, we can simplify further by expressing 9 as (3^2). Therefore, the equation becomes (3^2)^(x-12) = (3^x)^2.

Using the property of exponents again, the equation becomes 3^(2(x-12)) = (3^x)^2.

Since the bases on both sides of the equation are the same, we can equate their exponents. So, 2(x-12) = 2x.

Simplifying this equation, we get 2x - 24 = 2x.

Notice that the variable x canceled out on both sides of the equation. This means that the equation has no solution.

Therefore, the original equation 9^(x-12) = 3^x2 does not have a valid value for x that satisfies the equation.