To solve this equation, we can use the properties of logarithms. First, we can combine the logarithms on the left side of the equation using the product rule of logarithms:

log2(3x+1) * log3 x = 2 log2(3x+1)

Next, we can use the power rule of logarithms to rewrite the right side of the equation:

log2(3x+1)^2 = log2((3x+1)^2)

Now, we can set the two expressions equal to each other:

log2(3x+1) * log3 x = log2((3x+1)^2)

Since the bases of the logarithms are the same (both log2), we can drop the logarithms and set the arguments equal to each other:

log3 x = (3x+1)^2

Now, we can exponentiate both sides with base 3 to get rid of the logarithm:

x = 3^((3x+1)^2)

This equation cannot be solved algebraically, but you can approximate the solution using numerical methods or calculators.