https://file.aiquickdraw.com/mathbot/file/1727721390914axua3rxh.jpg

The equation provided is:

\[
6 = 4^x
\]

To express this in logarithmic form, we use the general rule:

\[
a^b = c \quad \text{can be written as} \quad \log_a(c) = b
\]

In your case, the base \(a = 4\), the exponent \(b = x\), and the result \(c = 6\). Thus, the equation in logarithmic form is:

\[
\log_4(6) = x
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you convert from logarithmic form back to exponential form?
2. What is the natural logarithm, and how is it different from other logarithms?
3. How can you calculate \(\log_4(6)\) using a calculator?
4. What are the properties of logarithms that can simplify expressions like \(\log_4(6)\)?
5. Can you use change of base formula to express \(\log_4(6)\) in terms of base 10 or base \(e\)?

**Tip:** The change of base formula can help when a calculator doesn't support a specific base: \(\log_b(a) = \frac{\log_c(a)}{\log_c(b)}\).

Learn how to convert the exponential equation 6 = 4^x into logarithmic form, following the general rule of logarithms. This problem covers key algebraic concepts suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation