Find x, if : (i) `log_(10) (x + 5) = 1`
(ii) `log_(10) (x + 1) + log_(10) (x - 1) = log_(10) 11 + 2 log_(10) 3`

Answer

To solve the given equations step by step, we will follow the properties of logarithms.

### Part (i): Solve `log_(10) (x + 5) = 1`

1. **Start with the equation**:
\[ \log_{10}(x + 5) = 1 \]

2. **Convert the logarithmic equation to exponential form**:
Using the property that if \(\log_b(a) = c\), then \(a = b^c\):
\[ x + 5 = 10^1 \]

3. **Simplify the right side**:
\[ x + 5 = 10 \]

4. **Isolate \(x\)**:
Subtract 5 from both sides:
\[ x = 10 - 5 \]
\[ x = 5 \]

### Solution for Part (i):
\[ x = 5 \]