Solve for x:


6 to the power of x=11



x=   
You may enter the exact value or round to 4 decimal places.

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

\[
6^x = 11
\]

we can take the natural logarithm (ln) of both sides:

\[
\ln(6^x) = \ln(11)
\]

Using the logarithmic identity \( \ln(a^b) = b\ln(a) \), we get:

\[
x \cdot \ln(6) = \ln(11)
\]

Now, solve for \( x \):

\[
x = \frac{\ln(11)}{\ln(6)}
\]

Using a calculator to evaluate the logarithms:

\[
x = \frac{\ln(11)}{\ln(6)} \approx \frac{2.3979}{1.7918} \approx 1.3384
\]

So, the solution is:

\[
x \approx 1.3384
\]

Would you like further details or clarifications?

Here are 5 related questions you may find interesting:
1. How do you solve exponential equations using logarithms?
2. Can you apply this method to other bases besides 6?
3. What are the properties of logarithms that are useful in solving equations?
4. How can you use logarithmic and exponential functions in real-life applications?
5. How do logarithmic scales work in scientific contexts?

**Tip:** Always remember to apply the properties of logarithms, like \( \ln(a^b) = b \ln(a) \), to simplify expressions with exponents.

Solve for x: 6 to the power of x = 11. x = ? You may enter the exact value or round to 4 decimal places.

Learn how to solve the exponential equation 6^x = 11 using logarithms. This detailed solution covers the application of logarithmic properties and the formula ln(a^b) = b * ln(a). Ideal for students in Grades 10-12, including step-by-step instructions and calculator approximations.

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