It's your turn on Equations with exponentials and logarithms

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf file below.

Exercise 1.

Solve the following equation [18left(frac{3^{x+1}}{2}-1right)=frac{7}{3^x}cdot 3^{2x+1}]

Exercise 2.

Solve the following equation [left(2-log_{frac{1}{2}}{sqrt[3]{x}}right)left(2+log_{frac{1}{2}}{sqrt[3]{x}}right)=log_{frac{1}{2}}{x}]

Exercise 3.

Solve the following equation [6^x-3^{x+1}-2^{x+1}+6=0] (Hint: (6^x-3^{x+1}-2^{x+1}+6=(3^x+a)(2^x+b)) for some suitable [a,b]…)

[This exercise is solved just in the pdf file below]