https://file.aiquickdraw.com/mathbot/file/1730202015538apt6qrm1.jpg

The problem presented is:

\[
\log_2(x - 12) = 4
\]

To solve for \( x \), follow these steps:

### Step 1: Rewrite the logarithmic equation in exponential form
Since \(\log_2(x - 12) = 4\), we can rewrite it as:
\[
x - 12 = 2^4
\]

### Step 2: Calculate \( 2^4 \)
\[
2^4 = 16
\]
So,
\[
x - 12 = 16
\]

### Step 3: Solve for \( x \)
Add 12 to both sides:
\[
x = 16 + 12
\]
\[
x = 28
\]

### Answer:
\[
x = 28
\]

Would you like further details, or do you have any questions about this process?

### Related Questions
1. How would you solve \( \log_3(x - 5) = 2 \)?
2. What if the equation was \( \log_5(2x + 1) = 3 \)?
3. How do you convert a logarithmic equation into an exponential equation?
4. What is the value of \( x \) in \( \log_4(x + 3) = 5 \)?
5. How can you solve equations involving natural logarithms, like \( \ln(x - 2) = 3 \)?

### Tip
When solving logarithmic equations, remember that \(\log_b(a) = c\) translates to \(a = b^c\). This is often the key step in finding solutions.

This page provides a step-by-step solution to the logarithmic equation log_2(x - 12) = 4, using the properties of logarithms and exponential equations. Ideal for high school students in 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