Logarithmic equations and inequalities

Solve the equation

$${\log }_2(x+5)={\log }_2(3x-1).$$

Solution available to those who have unlocked the subject.

Solve the equation

$${\log }_5(x^2-9)={\log }_5(3x+9).$$

Solution available to those who have unlocked the subject.

Solve the equation

$${\log }_3(x-2)=3.$$

Solution available to those who have unlocked the subject.

Solve the equation

$${\log }_{\frac{1}{2}}(x+3)=-2.$$

Solution available to those who have unlocked the subject.

Solve the equation

$${\log }_4(5x+1)=\frac{1}{2}.$$

Solution available to those who have unlocked the subject.

Solve the equation

$${\log }_{2}x+{\log }_2(x-6)=4.$$

Solution available to those who have unlocked the subject.

Solve the equation

$${\log }_3(x+2)-{\log }_3(x-4)=1.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$({\log }_{3}x{)}^2-4{\log }_{3}x+3=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$({\log }_{2}x{)}^2+{\log }_{2}x-2=0.$$

Solution available to those who have unlocked the subject.

Solve the inequality

$${\log }_2(3x-1)>3.$$

Solution available to those who have unlocked the subject.

Solve the inequality

$${\log }_{\frac{1}{3}}(x-2)\ge -1.$$

Solution available to those who have unlocked the subject.

Solve the inequality

$${\log }_{\frac{1}{2}}(x+1)<{\log }_{\frac{1}{2}}(2x-3).$$

Solution available to those who have unlocked the subject.