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

Using RQ^2 = (RS)(RP) <--- That's the length of a secant and chord

to find RQ (You already know the length of RS and RP, because they are labelled,

Then using pythagoras theorem, find PQ

PR² = PQ² + QR²

26² = PQ² + 364

PQ² = 312

PQ = 2sqrt(78)