(5/3)^6x+2=(9/25)^-x+2

Question

Given the exponential equation:(5/3)^6x+2=(9/25)^-x+2, find a common base and solve for x.
a) -2/3
b) -3/2
c) 3/2
d) 2/3

Answer 1

(5/3)^6x+2 = (3/5)^2(-x+2)            (Step 1: Write 9/25 as the perfect square)

 

(5/3)^6x+2 = (3/5)^{-2(x - 2)}        (step 2: bases are reciprocal of each other so factor out the negative sign)

 

(5/3)^6x+2 = (5/3)^2(x-2)            (Step 3: Use the law of exponent for negative exponent. (x)^-n = 1/xⁿ)

 

6x + 2 = 2(x - 2)                  (Step 4: Solve for x :-)