Which equation is equivalent to

equivalent to (1/3) ^x=27^x+2

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