Answer:
x=\frac{-3}{2}
Step-by-step explanation:
We have been given with the expression (1/3)^x=(27)^x+2
Now, to solve the equation firstly we have to make the base same on both sides
(1/3)^x=3^{-x}
27 can be written as 3^3
27^x=(3^3)^x=3^{3x}
Hence, given expression can be rewritten as
3^{-x}=3^{3(x+2)}
Now since, base is same we can equate the powers on both sides
-x=3(x+2)\\ \Rightarrow-x= 3x+6\\ \Rightarrow -x-3x=6\\-4x=6\Rightarrow x=\frac{-3}{2}
Therefore given expression (1/3)^x=(27)^x+2 is equivalent to x=\frac{-3}{2}
Equivalent means the simplified form of any given expression
