Question

How do you solve the given equation. If necessary, round to four decimal places.

log5 (x + 2) – log5 8 = log5 64

Answer 1

To solve the equation log5 (x + 2) - log5 8 = log5 64, combine the logarithms on the left side, set the inside expressions equal to each other, and solve for x.

Step-by-step explanation:

To solve the equation log5 (x + 2) - log5 8 = log5 64, we can use the logarithmic properties.

1. Combine the two logarithms on the left side using the property log(a) - log(b) = log(a/b). This gives us log5 ((x + 2)/8) = log5 64.
2. Since the logarithms have the same base, we can set the inside expressions equal to each other. (x + 2)/8 = 64.
3. Multiply both sides by 8 to get x + 2 = 512.
4. Subtract 2 from both sides to isolate x. x = 510.

Therefore, the solution to the equation is x = 510.