# EXPS 1 | Lesson 4 | Practice Solutions

1. $$2^x=32$$, then $$2^x=2^5 ; x=5$$
2. $$2^x=4^2$$, then $$2^x=(2^2)^2$$, then $$2^x=2^4 ; x=4$$
3. $$4^{x-1}=16^3$$, then $$4^{x-1}=(4^2)^3$$, then $$4^{x-1}=4^6$$, then $$x-1=6 ; x=7$$
4. $$5^{\frac x2}=125$$, then $$5^{\frac x2}=5^3$$, then $$\dfrac x2= 3 ; x =6$$
5. $$3^{2-x}=27$$, then $$3^{2-x}=3^3$$, then $$2-x=3 ; x=-1$$
6. $$2^{x+2}=8^x$$, then $$2^{x+2}=(2^3)^x$$, then $$2^{x+2}=2^{3x}$$, then $$x+2=3x ; x=1$$
7. $$2^{2x-1}=8^3$$, then $$2^{2x-1}=(2^3)^3$$, then $$2x-1=9 ; x=5$$
8. $$2^{3x-1}=4^{x+3}$$, then $$2^{3x-1}=(2^2)^{x+3}$$, then $$2^{3x-1}=2^{2x+6}$$, then $$3x-1=2x+6 ; x=7$$