I'm lost on how to solve this equation

Question

2^1-x=8^3x+1

Answer 1

Would it help if I reminded you that 8 is 2³? 

 

;)

Answer 2

2^(1-x)=8^(3x+1)

8=2^3

2^(1-x)=(2^3)^(3x+1)

2^(1-x)=2^(3*(3x+1))

2^(1-x)=2^(9x+3)

since the bases are the same the exponents are equal to each other

(1-x)=(9x+3)

1-x=9x+3

1=9x+x+3)

1=10x+3

1-3=10x

-2=10x

x=-2/10

x=(-1/5) answer

check: 2^(1-(-1/5))=2^(6/5) left side

8^(3(-1/5)+1)

8^(-3/5+1)

8^(2/5)

(2^3)^(2/5)

2^(6/5) right side