log (1.5x + 14) + log (2) = 0.5 log (x^4)
Other than a slight mistake, you were on the right track..... let's go from your last step
log (3x + 28) = 0.5 * 4 log (x)
log (3x + 28 ) = 2 * log (x)
Let's write the "2" back as an exponent
log (3x + 28) = log (x^2)
Since the we have a single log on each side....we can forget those and solve this :
3x + 28 = x^2 rearranging, we have that
x^2 - 3x - 28 =0 this is factorable as
(x -7) ( x+4) = 0
Setting both factors to 0 and solving for x, we have that x = 7 or x = -4
Note that both solutions will solve the simplified form of the problem ,i.e., log (3x + 28) = log (x^2) !!!!
!
