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The image contains a mathematical problem written in Hindi. The equation is:

\[
7^x = 8^3 \text{ होने पर } x \text{ का मान कितना होगा?}
\]

Translation:

Given that \(7^x = 8^3\), what is the value of \(x\)?

### Solution:

To solve for \(x\), we start with the given equation:

\[
7^x = 8^3
\]

First, simplify \(8^3\):

\[
8^3 = 512
\]

So the equation becomes:

\[
7^x = 512
\]

Now, to find \(x\), we take the logarithm (log base 7) of both sides:

\[
x = \log_7{512}
\]

To calculate \(x\), we'll use the change of base formula:

\[
x = \frac{\log{512}}{\log{7}}
\]

Now we can compute the logarithms:

\[
\log{512} \approx 2.7095 \quad \text{and} \quad \log{7} \approx 0.8451
\]

So:

\[
x \approx \frac{2.7095}{0.8451} \approx 3.206
\]

Thus, the value of \(x\) is approximately \(3.206\).

Would you like more details or have any questions?

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**Related Questions:**
1. How would the calculation change if the equation was \(7^x = 9^3\)?
2. Can you solve \(7^x = 512\) using natural logarithms?
3. What is the general method to solve equations of the form \(a^x = b\)?
4. How does the change of base formula work in logarithms?
5. How do logarithms help in solving exponential equations?

**Tip:** Understanding the change of base formula can be very helpful when dealing with logarithms of different bases!

7^x = 8^3 होने पर x का मान कितना होगा?

Learn how to solve the exponential equation 7^x = 8^3 step by step using logarithms and the change of base formula. This problem is ideal for students in Grades 9-12 and covers key concepts in algebra and logarithms.

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