Answer:
Explanation
1. Start by applying the quotient rule of logarithms, which states that log base a of b divided by c is equal to log base a of b minus log base a of c. In this case, a is 2, b is (10x + 5), and c is 5.
So, log2 (10x + 5) − log2 5 = log2 [(10x + 5) / 5]
2. Simplify the expression inside the logarithm by dividing (10x + 5) by 5.
log2 [(10x + 5) / 5] = log2 (2x + 1)
The expression (10x + 5) / 5 simplifies to (2x + 1).
3. The simplified expression is now log2 (2x + 1).
This means that log2 (10x + 5) − log2 5 is equal to log2 (2x + 1).
Therefore, the solution to the equation log2 (10x + 5) − log2 5 is log2 (2x + 1).