Solve the equation 1^2x-4=2^3x+1. Then check your answer using proper checking techniques.

Question

Solve the equation 1^2x-4=2^3x+1. Then check your answer using proper checking techniques.

Answer 1

1 to any power is still 1

left side reduces to 1-4 =-3

right side is 2^3x + 1

-3 = 2^3x + 1

2^3x = -4

that has no solution. graph 2^3x and it never goes below the x axis, it's never negative

so maybe the right side was really 2^(3x+1)

and the left side was really 1^(2x-4)

then 1= 2^(3x+1)

and 3x + 1 = 0

3x =-1

x = -1/3

It doesn't matter what x is, the left side is still just 1. 1 to any power is 1

the right side needs to have 2 to the zero power. any number to the zero power = 1

3(-1/3)+ 1 = -1+1 = 0