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?

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!