5. Solve: log 5 (8r-7) = log 5 (r^2 + 5):
A. r = 2 or r = 6
B. r = -2 or r = 6
C. r = -2 or r = -6
D. r = 3 or r = 4
To solve the given equation, we can use the property of logarithms that states that if two logarithms with the same base are equal, then their arguments must be equal as well. In this case, we have:
log5(8r-7) = log5(r^2 + 5)
So we can set the arguments of the logarithms equal to each other:
8r-7 = r^2 + 5
Rearranging the equation gives us:
r^2 - 8r + 12 = 0
To solve this quadratic equation, we can factorize it or use the quadratic formula. In this case, we will factorize it:
(r-2)(r-6) = 0
Now we can set each factor equal to zero and solve for r:
r-2 = 0 or r-6 = 0
If we add 2 to both sides of the first equation, we get:
r = 2
If we add 6 to both sides of the second equation, we get:
r = 6
Therefore, the solutions to the equation are r = 2 and r = 6.
So the answer is A. r = 2 or r = 6.