8^x+1 = 4•6^x

Question

We have to solve it for a real number and if not we are supposed to leave it in logarithmic form 

Answer 1

 

8^x+1= 4*6^x

 

or (2³)^x+1 = 2².2^x.3^x

 

or 2^3x+3 = 2^x+23^x

 

or 2^3x+3 /2^x+2 = 3^x

 

or 2^2x+1=3^x

or (2x+1) ln2 =  xln3

or  x*(2ln2  -ln3) = -ln2

x=-ln2/(2ln2 -ln3) = - .693/(.693*2 - 1.0986) = -2.411