First step, combine the like bases:

Now use laws of exponents to take out "like parts". and so

where the value inside the parentheses is a number you can calculate directly. Do the same thing on the right so you get something like where "A" and "B" are specific numbers. Finally, take logarithms of both sides.

Added: the "A" and "B" are which, according to my calculator is 1.8900 (to four decimal places) and [tex]B= 3^{-1/2}- 3^{-3/2}= 0.3849.

Your equation is taking logarithms of both sides, log(1.8900)+ (log(2)/3)x= log(0.3849)+ (log(3)/2)x. You can use either common or natural logarithms and get the correct answer.