https://file.aiquickdraw.com/mathbot/file/1726085797526wwcbl4c5.jpg

The equation presented in the image is:

\[
\log_{3x} \left( x^2 + 4x + 15 \right) = 2
\]

To convert a logarithmic equation to its exponential form, we follow the rule:

\[
\log_b(a) = c \quad \Rightarrow \quad a = b^c
\]

Here, \(b = 3x\), \(a = x^2 + 4x + 15\), and \(c = 2\).

Using this rule, we can rewrite the equation as:

\[
x^2 + 4x + 15 = (3x)^2
\]

This is the exponential form of the given logarithmic equation.

Would you like more details on how to proceed with solving this equation or breaking it down further?

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Here are 5 related questions that may help you explore further:
1. How do you solve quadratic equations after expansion?
2. What are the properties of logarithms that might simplify such equations?
3. How do exponential and logarithmic functions relate to each other graphically?
4. How does changing the base in a logarithmic function affect the corresponding exponential equation?
5. Can logarithmic functions have negative bases?

**Tip:** Remember, to switch from logarithmic to exponential form, always use the structure: \( \log_b(a) = c \) translates to \( a = b^c \).

Write the log equation as an exponential equation. You do not need to solve for x. log_{3x} (x^2 + 4x + 15) = 2

Learn how to convert the logarithmic equation log_{3x}(x^2 + 4x + 15) = 2 into its exponential form. This problem involves understanding the properties of logarithms and converting them to exponential equations, suitable for students in Grades 9-12.

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