To solve the equation \( y = 2^x \) for \( x \), we can use logarithms. Specifically, we apply the logarithm to both sides of the equation to isolate \( x \).

### Step 1: Apply the natural logarithm (or log base 2)
We can take the natural logarithm (denoted as \( \ln \)) of both sides, or take the logarithm base 2 directly. Here, I'll use the natural logarithm:

\[
\ln(y) = \ln(2^x)
\]

### Step 2: Use the logarithmic property
Use the property of logarithms \( \ln(a^b) = b \ln(a) \) to bring down the exponent on the right side:

\[
\ln(y) = x \ln(2)
\]

### Step 3: Solve for \( x \)
To isolate \( x \), divide both sides of the equation by \( \ln(2) \):

\[
x = \frac{\ln(y)}{\ln(2)}
\]

Thus, the solution for \( x \) is:

\[
x = \frac{\ln(y)}{\ln(2)}.
\]

### Final Answer:
\[
x = \frac{\ln(y)}{\ln(2)}.
\]

This is the solution for \( x \) in terms of \( y \).

Would you like further clarification or examples? Here are 5 related questions for exploration:

1. How do you solve \( y = 10^x \) for \( x \)?
2. What happens if the base of the exponential function is \( e \), i.e., \( y = e^x \)?
3. How do you solve for \( x \) when \( y = 3^x \)?
4. How do logarithms help in solving exponential equations?
5. What is the inverse of the exponential function \( y = 2^x \)?

**Tip:** To solve for \( x \) in exponential equations, always apply logarithms to isolate the variable in the exponent!

Learn how to solve the exponential equation y = 2^x for x using logarithms. This solution includes step-by-step instructions for applying logarithms to isolate x, with a focus on the natural logarithm and its properties. Suitable for students in Grades 9-11.

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