https://file.aiquickdraw.com/mathbot/file/172956711490989h7s62c.jpg

The equation provided is:

\[
3 \log_2{(x - 1)} + \log_2{4} = 5
\]

Let's solve this step-by-step:

### Step 1: Simplify \(\log_2{4}\)
We know that \(\log_2{4} = 2\) because \(2^2 = 4\). So, the equation becomes:

\[
3 \log_2{(x - 1)} + 2 = 5
\]

### Step 2: Subtract 2 from both sides
\[
3 \log_2{(x - 1)} = 5 - 2
\]
\[
3 \log_2{(x - 1)} = 3
\]

### Step 3: Divide both sides by 3
\[
\log_2{(x - 1)} = 1
\]

### Step 4: Solve the logarithmic equation
\(\log_2{(x - 1)} = 1\) implies:
\[
x - 1 = 2^1
\]
\[
x - 1 = 2
\]
\[
x = 3
\]

### Final Answer:
The solution is \(x = 3\).

---

Would you like more details on any step or do you have any other questions? 

Here are 5 related questions for further exploration:
1. How do you solve equations with logarithms in different bases?
2. What happens if a logarithmic term has a negative argument?
3. How do you graph logarithmic functions like \(\log_2(x-1)\)?
4. How does the change of base formula work in logarithms?
5. What are the key properties of logarithmic functions that simplify solving equations?

**Tip:** Always check that the argument of the logarithmic function (here \(x - 1\)) remains positive since logarithms are undefined for non-positive numbers!

Solve the equation: 3log₂(x-1) + log₂(4) = 5

This article provides a step-by-step solution to the logarithmic equation 3log₂(x-1) + log₂(4) = 5. Learn about key concepts in logarithms, including simplifying logarithmic expressions and solving for unknowns. Suitable for high school students (Grades 10-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation