https://file.aiquickdraw.com/mathbot/file/1730165224287nkrfj2vq.jpg

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.

Use rules of logarithms to combine into a single logarithm (if necessary), then solve for x: a. log(x) - log(3) = 1, b. log(2x + 5) - log(x + 7) = 0

This page covers solving logarithmic equations by applying properties of logarithms to combine terms. Learn how to solve equations such as log(x) - log(3) = 1 and log(2x + 5) - log(x + 7) = 0 with step-by-step solutions, focusing on the application of logarithmic properties and exponential conversion. Suitable for high school students in Grades 10-12.

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