Given: log103+log10(4x+2)=log10(x+4)+1 Consider the L.H.S, log103+log10(4x+2) by using the product rule we get, log103+log10(4x+2)=log10(3.(4x+2))=log10(12x+6) ......(1) Now consider the R.H.S, log10(x+4)+1 As we know that, a=logbba ⇒1=log1010 ⇒log10(x+4)+1=log10(x+4)+log1010 Using the product rule, log10(x+4)+1=log10((x+4).10) =log10(10x+40).......(2) By using (1) and (2) in log103+log10(4x+2)=log10(x+4)+1 we get, log10(12x+6)=log10(10x+40) Cancelling out the log on both sides we get, 12x+6=10x+40 ⇒12x−10x=40−6 ⇒2x=34 ⇒x=17