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The problem shown in the image is asking to rewrite the exponential equation \( 36^x = 6 \) in logarithmic form.

To convert an exponential equation to logarithmic form, the general rule is:

\[
a^x = b \quad \text{is equivalent to} \quad \log_a(b) = x
\]

For the given equation \( 36^x = 6 \), using this rule:

\[
\log_{36}(6) = x
\]

So, the correct answer is the option:
\[
\log_{36}(6) = x
\]

This corresponds to the fourth option on the list.

Would you like further details on logarithmic and exponential relationships or have any questions?

Here are 5 related questions to explore:
1. How do you convert logarithmic equations back into exponential form?
2. What is the logarithmic form of \( 10^x = 100 \)?
3. How do you solve for \( x \) in logarithmic equations?
4. How does changing the base in an exponential equation affect the logarithmic form?
5. How can logarithms be used to solve real-world growth or decay problems?

**Tip:** To solve logarithmic equations, you can often use properties like the product, quotient, or power rules of logarithms.

What is the equation rewritten in logarithmic form for the exponential equation 36^x = 6?

This tutorial explains how to rewrite the exponential equation 36^x = 6 in logarithmic form. Learn the conversion process using key formulas such as a^x = b is equivalent to log_a(b) = x. Ideal for students in grades 9-12 studying logarithms and exponents.

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