https://file.aiquickdraw.com/mathbot/file/17265849695621jfxofop.jpg

The given equation in the image is:

\[
\log_2 x = -5
\]

To convert this logarithmic equation into an exponential equation, recall the general logarithmic definition:

\[
\log_b a = c \quad \text{means} \quad a = b^c
\]

In this case:

\[
\log_2 x = -5
\]

This means that \(x = 2^{-5}\).

Now, solving for \(x\):

\[
x = \frac{1}{2^5} = \frac{1}{32}
\]

Thus, the equivalent exponential equation is:

\[
x = 2^{-5}
\]

Would you like further details or clarifications?

Here are 5 related questions to explore:

1. How do you convert any logarithmic equation to an exponential form?
2. What is the relationship between logarithms and exponents?
3. What is the value of \( \log_2(32) \)?
4. How would you solve for \( x \) if \( \log_3 x = 4 \)?
5. Can you explain the properties of logarithms that make solving these equations possible?

**Tip:** When converting from a logarithmic to an exponential equation, always remember that the base of the logarithm becomes the base of the exponent.

Convert log equation into exponential equation. log_2(x) = -5

Learn how to convert the logarithmic equation log_2(x) = -5 into its exponential form. This solution demonstrates the relationship between logarithms and exponents, explaining how log_b(a) = c translates to a = b^c. Suitable for students in Grades 9-12.

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