Answer:
To solve the equation (log3 x)^2 - 4 log3 x + 3 = 0, let's make a substitution.
Let's assume log3 x = y, such that x = 3^y.
Now, substitute this value back into the equation:
(y)^2 - 4(y) + 3 = 0.
To solve this quadratic equation, we can factor it:
(y - 1)(y - 3) = 0.
Setting each factor equal to zero gives us:
y - 1 = 0 or y - 3 = 0.
For y - 1 = 0,
y = 1.
Substituting y = 1 back into our assumption, we get:
log3 x = 1.
Now, let's solve for x:
x = 3^(1).
x = 3.
For y - 3 = 0,
y = 3.
Substituting y = 3 back into our assumption, we get:
log3 x = 3.
Now, let's solve for x:
x = 3^(3).
x = 27.
So the solutions to the equation are x = 3 and x = 27.
Explanation: