x=1.041247503

LOG IS NATURAL LOG with LOG10 there is no solution

LN(4)+LN(17x+1)=LN(3x+7)+11-9

SIMPLIFIES TO

LN(4)+LN(17x+1)=LN(3x+7)+2 . .............(1) Taking 2 to be LN(e^2) we have

LN(17x+1)-LN(3x+7)=LN(e^2)-LN(4)

or LN((17x+1)/(3x+7))=LN((e^2)/4) hence

(17x+1)/(3x+7)=(e^2)/4 solution gives x=1.041247503

substituting this value of x into function y= LN(4)+LN(17x+1)-LN(3x+7)-2 gives y=-9.50891800410858E-07 which is as good as zero