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.