Answer:
≈ 1.13
Explanation:
To solve this equation, we can start by simplifying the left-hand side using the laws of exponents. We have:
2(1/49)^(r-2) = 2^(1-2) * (1/49)^(r-2) = (1/2^2) * (49^-(r-2)) = (1/4) * (49^-(r-2))
Now we can substitute this expression into the original equation and simplify further:
2(1/49)^(r-2) = 14
(1/4) * (49^-(r-2)) = 14
49^-(r-2) = 56
To isolate the variable on one side of the equation, we can take the logarithm of both sides with base 49:
log49(49^-(r-2)) = log49(56)
-(r-2) = log49(56)
r - 2 = -log49(56)
r = 2 - log49(56)
Therefore, the solution to the equation is:
r = 2 - log49(56) ≈ 1.13