Solve: log 5 (8r-7) = log 5 (r^2 + 5):
To solve the equation log₅(8r-7) = log₅(r² + 5), we can use the property of logarithms that states if logₐ(b) = logₐ(c), then b = c.
So, in this case, log₅(8r-7) = log₅(r² + 5) implies that 8r-7 = r² + 5. We can now solve this equation for r.
First, simplify the equation: r² - 8r + 12 = 0.
Next, we can factor the quadratic equation: (r-2)(r-6) = 0.
Now solve for r:
1) r-2 = 0: Add 2 to both sides: r = 2.
2) r-6 = 0: Add 6 to both sides: r = 6.
Therefore, the two solutions to the equation log₅(8r-7) = log₅(r² + 5) are r = 2 and r = 6.