Let's try the following method. We'll subtract log 3 (2) both sides:

log 3 (x) = 2 - log 3 (2)

We'll re-write 2 as:

2 = 2*1

We'll substitute the value 1 by log 3 (3).

2 = 2*log 3 (3)

We'll use the power property of the logarithms:

2 = log 3 (3)^2

We'll re-write the equation:

log 3 (x) = log 3 (3)^2 - log 3 (2)

Because the bases are matching, we'll transform the difference of logarithms from the right side, into a quotient:

log 3 (x) = log 3 (9/2)

Because the bases are matching, we'll apply the one to one property:

x = 9/2

**x = 4.5**

Since the value of x is positive, the solution of the equation is valid.

Here we use the relation log A + log B= log A*B

( log refers to logarithm to the base 3)

log x + log 2 = 2

=> log (2*x) = 2

Raise the left and right hand sides to the power of 3.

3^ log (2*x) = 3^2

=> 2x = 9

=> x= 9/2

**Therefore x = 9/2**

To solve for x. log3(x)+log4(2) = 2

We rewrite the right side of the equation 2 as log base3. So 2= log3 (3^2). So the equation becomes:

log3(x)+log3(2) = log3 (3^2).

log3 (x*2) = log3 (9) , as loga+logb = log(ab).

Take antilog.

2x = 9.

x = 9/2.