To solve the equation, we can use the properties of logarithms to simplify the expression:

log3 X + 2log3 (9X) = 7

Use the power rule of logarithms: log_a (A^n) = n * log_a (A)

log3 X + log3 ((9X)^2) = 7
log3 X + log3 (81X^2) = 7

Combine the logarithms using the product rule: log_a (A) + log_a (B) = log_a (A*B)

log3 (X * 81X^2) = 7
log3 (81X^3) = 7

Rewrite the equation in exponential form: a^b = c is equivalent to log_a c = b

3^7 = 81X^3

Solve for X:

2187 = 81X^3

Divide both sides by 81:

27 = X^3

Take the cube root of both sides:

X = 3

Therefore, the solution to the equation log3 X + 2log3 (9X) = 7 is X = 3.