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# A-Level Maths | Logs
- URL: https://www.a-level-maths-tutor.com/a-level-maths-logs/
- Published: 2026-03-24T16:20:48.000Z
- Updated: 2026-07-25T10:25:06.000Z
- Author: Jaisul Naik
- Tags: Pure Maths

### Exponential graph

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-6.png)

### Rules of Logarithms

1. **log(a) + log(b) = log(ab)**
2. **log(a) - log(b) = log(a/b)**
3. **log(a)n \= nlog(a)**
4. **loga(a) = 1**
5. **If loga(x) = 5 then x = a5**

---

## Power rule

### Question 1

**hint: use rule 3**

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-24-at-16.20.14@2x.png)

## Adding and subtracting logs

### Question 2a

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-24-at-15.56.04@2x.png)

### Question 2b

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-24-at-15.53.35@2x.png)

## Solving exponential equations

### Question 3a

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-24-at-16.02.51@2x.png)

### Question 3b

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-24-at-16.03.16@2x.png)

## Solving log equations

### Question 4a

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-24-at-16.31.11@2x.png)

### Question 4b

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-24-at-16.12.13@2x-1.png)

**Answers x=0.5, y=0.6**

### Question 4c

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-24-at-16.12.21@2x-1.png)

**Answers: x=1, y=5/3**

### Question 4d

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-7-1.png)

### Question 4e

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/image-8-1.png)

## Modelling with logs

### Question 5a

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-31-at-16.06.15@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-31-at-16.06.21@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-31-at-16.06.25@2x.png)

### Question 5b

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-31-at-16.09.04@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-31-at-16.09.10@2x.png)

![](https://storage.ghost.io/c/37/0e/370e4698-c6d5-4470-8b24-7d14723fff86/content/images/2026/03/CleanShot-2026-03-31-at-16.09.14@2x.png)

---

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