https://file.aiquickdraw.com/mathbot/file/172434865141845m8y8tr.jpg

The equation provided is:

\[
\log_2 (3x - 1) = 3
\]

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

1. Recall that the logarithmic equation \(\log_b(a) = c\) can be rewritten in its exponential form as \(a = b^c\).

   For the given equation:

   \[
   3x - 1 = 2^3
   \]

2. Calculate \(2^3\):

   \[
   3x - 1 = 8
   \]

3. Solve for \(x\):

   \[
   3x = 8 + 1
   \]
   \[
   3x = 9
   \]
   \[
   x = \frac{9}{3} = 3
   \]

So, the solution is:

\[
x = 3
\]

Would you like more details or have any other questions?

Here are some related questions you might find useful:
1. How do you solve logarithmic equations with different bases?
2. What are the properties of logarithms and how are they used in equations?
3. Can logarithmic functions have negative arguments?
4. How do you graph logarithmic functions?
5. How does the change of base formula work in logarithms?

**Tip:** When dealing with logarithmic equations, always check if the argument of the logarithm is positive, as logarithms are only defined for positive numbers.

Learn how to solve the logarithmic equation log2 (3x - 1) = 3 with a detailed step-by-step solution. This problem involves logarithms and exponential equations, showing how to convert logarithmic equations into their exponential form and solve them effectively. Suitable for 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