Solve for X: Finding the Value in x ln(7) Equation

To solve this problem, we'll follow the steps outlined:

• Step 1: Recognize that the expression $x \ln 7$ can be thought of in terms of the power property of logarithms, which helps reframe it into a single logarithm.
• Step 2: Apply the formula $\ln(a^b) = b \ln a$. This tells us that if we have something of the form $b \ln a$, we can express it as $\ln(a^b)$.
• Step 3: Utilize the known expression and rule by substituting $a = 7$ and $b = x$. Thus, $x \ln 7$ becomes $\ln(7^x)$.

Therefore, the rewritten expression for $x \ln 7$ using logarithm rules is $\ln 7^x$.

This matches choice 4 from the provided options.