3 raise to power 3x minus 8=1/3 raise to power x minus 2

Answer 1

To solve the equation 3^(3x) - 8 = (1/3)^(x-2), we can rewrite the right side of the equation using the property 1/(a^b) = (a^(-b)).

Thus, the equation becomes:
3^(3x) - 8 = 3^(-x+2)

Now we can set the bases equal to each other:
3^(3x) = 3^(-x+2)

Since the bases are equal, we can set the exponents equal to each other:
3x = -x + 2

Now solve for x:
4x = 2
x = 1/2

Therefore, the solution to the equation is x = 1/2.

Answer 2

You have the steps
3^(3x) - 8 = 3^(-x+2)
3^(3x) = 3^(-x+2)
what happened to the -8?

I think the equation was supposed to be 3^(3x - 8) = 3^(-x+2)
If so, then we have
3x-8 = -x+2
4x = 10
x = 5/2

Answer 3

Apologies for the mistake in my response. You are correct in identifying the error in how I wrote the equation.

The correct equation is indeed 3^(3x - 8) = 3^(-x+2).

Following your steps:

3x - 8 = -x + 2

Combining like terms:

4x - 8 = 2

Adding 8 to both sides:

4x = 10

Dividing both sides by 4:

x = 10/4

Simplifying:

x = 5/2

Therefore, the correct solution to the equation is x = 5/2.