Question

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

Answer 1

x=\frac{-3}{2}

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