The given equation is:

$\log_7(x) = 2$

To solve for $x$, we can rewrite the logarithmic equation in its exponential form. The general form is:

$\log_b(a) = c \Rightarrow a = b^c$

So, applying this to our problem:

$x = 7^2$

Calculating $7^2$:

$x = 49$

Solution

The positive value of $x$ is: $x = 49$

Would you like more details on logarithmic functions or have any questions?

Here are some related questions to explore:

1. How do we solve equations with logarithms involving different bases?
2. What is the process of solving logarithmic equations with variables on both sides?
3. How would the solution change if the equation were $\log_7(x) = -2$?
4. How does the concept of logarithmic and exponential functions apply to real-world problems?
5. Can you solve a logarithmic equation if the base is a fraction?

Tip: Remember, logarithmic equations can often be solved by rewriting them in exponential form, which helps isolate the variable more easily.