81^3(x+1)=9^2(x-1)
Solve this equation by expressing both sides as powers of 3.
To solve the equation 81^3(x+1) = 9^2(x-1), we can rewrite both sides of the equation as powers of 3.
Let's start by expressing 81^3 and 9^2 as powers of 3:
81^3 = (3^4)^3 = 3^(4*3) = 3^12
9^2 = (3^2)^2 = 3^(2*2) = 3^4
Now we can substitute these expressions back into the equation:
3^12(x+1) = 3^4(x-1)
Since the bases (3) are the same on both sides, we can equate the exponents:
12(x+1) = 4(x-1)
Distribute the multiplications:
12x + 12 = 4x - 4
Now let's isolate the variable (x).
Subtract 4x from both sides:
12x - 4x + 12 = -4
Combine like terms:
8x + 12 = -4
Subtract 12 from both sides:
8x = -4 - 12
Simplify:
8x = -16
Finally, divide by 8 to solve for x:
x = -16/8
Simplify further:
x = -2
Therefore, the solution to the equation is x = -2.