how do I solve the equation 2^(3x+1) = 8^p

Question

How do I solve the above equation for x in terms of p? Please show the steps in working it out. thanks.

Answer 1

2^3x+1 = 8^p

 

Now 8 = 2³, so we can re-write the equation as:

 

2^3x+1 = (2³)^p

2^3x+1 = 2^3p

 

Hence the exponents must be equal:

 

3x+1 = 3p

3x = 3p - 1

 

x = p - 1/3

 

Check:

2^3x+1

Substitute p - 1/3 for x:

2^{3(p - 1/3)+1} = 2^3p-1+1 = 2^3p = (2³)^p = 8^p

 

Check!