Solve for x. 
2Superscript xequals21
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Part 1
Solve for x.

To solve for \( x \) in the equation:

\[
2^x = 21
\]

we will use logarithms to find the value of \( x \).

### Step-by-Step Solution:

1. **Take the logarithm of both sides:**

   We can use the logarithm with any base, but for convenience, we typically use the natural logarithm (\( \ln \)) or the common logarithm (\( \log \)):

   \[
   \ln(2^x) = \ln(21)
   \]

2. **Apply the logarithm power rule:**

   The power rule of logarithms states that \( \ln(a^b) = b \ln(a) \). Applying this rule gives:

   \[
   x \ln(2) = \ln(21)
   \]

3. **Solve for \( x \):**

   Now, divide both sides by \( \ln(2) \):

   \[
   x = \frac{\ln(21)}{\ln(2)}
   \]

4. **Calculate the value:**

   Using a calculator, find the logarithm values:

   \[
   \ln(21) \approx 3.0445, \quad \ln(2) \approx 0.6931
   \]

   So:

   \[
   x \approx \frac{3.0445}{0.6931} \approx 4.39
   \]

### Final Answer:

\[
x \approx 4.39
\]

Would you like more details or have any other questions? Here are some related questions you might be interested in:

1. How to solve exponential equations with different bases?
2. How to use logarithms to solve equations in base 10?
3. What are the properties of logarithms and how are they useful in solving equations?
4. How can exponential growth models be solved using logarithms?
5. How do different bases (like base 2 or base e) affect solving equations?

**Tip:** Remember that logarithms are powerful tools for solving equations where the variable is an exponent.

Learn how to solve the exponential equation 2^x = 21 step by step using logarithms. This problem covers key algebraic concepts like the logarithm power rule and solving for variables in the exponent. Ideal for students in Grades 9-12.

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