https://file.aiquickdraw.com/mathbot/file/1726598613590c128ap67.jpg

The problem given is:

\[
\log_6 x = 3
\]

To solve for \(x\), we rewrite this logarithmic equation in its exponential form. The logarithmic statement \(\log_6 x = 3\) implies:

\[
x = 6^3
\]

Calculating this:

\[
x = 216
\]

So, the solution is:

\[
x = 216
\]

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions that could further expand on this concept:

1. How do you convert logarithmic equations to exponential form in general?
2. What is the general formula for solving \(\log_b x = y\)?
3. How do logarithms with different bases relate to each other (e.g., converting \(\log_6 x\) to base 10)?
4. How would you solve a logarithmic equation if the logarithm has an unknown base?
5. What is the significance of logarithmic functions in real-world applications?

**Tip:** Remember, \(\log_b x = y\) is the same as saying \(b^y = x\). This conversion between logarithmic and exponential forms is crucial in solving logarithmic equations.

Learn how to solve the logarithmic equation log_6(x) = 3. The solution involves converting the logarithmic form into exponential form, using the formula log_b(x) = y ↔ b^y = x. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation