To solve each equation, let's break down each part.

Part (a)

Given: $\log(x) - \log(3) = 1$

Combine the logs: $\log\left(\frac{x}{3}\right) = 1$

Rewrite in exponential form: $\frac{x}{3} = 10^1$ $\frac{x}{3} = 10$

Solve for $x$: $x = 30$

So, the answer is: $x = 30$

Part (b)

Given: $\log(2x + 5) - \log(x + 7) = 0$

Combine the logs: $\log\left(\frac{2x + 5}{x + 7}\right) = 0$

Rewrite in exponential form: $\frac{2x + 5}{x + 7} = 10^0$ $\frac{2x + 5}{x + 7} = 1$

Solve for $x$: $2x + 5 = x + 7$ $x = 2$

So, the answer is: $x = 2$

Let me know if you need any detailed explanations on these steps or have any questions!

Here are 5 related questions to expand on this topic:

1. What are the properties of logarithms used to combine or separate terms?
2. How do you convert a logarithmic equation to its exponential form?
3. What are the restrictions for the values of $x$ in logarithmic functions?
4. How do you solve logarithmic equations that have multiple terms with different bases?
5. What are common mistakes to avoid when solving logarithmic equations?

Tip: Always check if the solutions satisfy the domain of the original logarithmic expressions, as log functions require positive arguments.