Exponential equations and inequalities

Solve the equation

$$2^x=32.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$3^{x+2}=27^x.$$

Solution available to those who have unlocked the subject.

Solve the equation

$${\left(\frac{1}{4}\right)}^x=8^{x-1}.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$5^x=2.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$2^{3x-1}=6.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$7\cdot 3^x=4.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$9^x-10\cdot 3^x+9=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$4^x+2^x-6=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$2^x+2^{2-x}=5.$$

Solution available to those who have unlocked the subject.

Solve the inequality

$$5^{2x+1}\ge 125.$$

Solution available to those who have unlocked the subject.

Solve the inequality

$${\left(\frac{1}{3}\right)}^{2x-1}<9.$$

Solution available to those who have unlocked the subject.

Solve the inequality

$$4^x-2^{x+2}+3\le 0.$$

Solution available to those who have unlocked the subject.