Solving logarithmic equation

Question

52x-(51+50).5x+51=0
And my answer just simply rewrite into (5x)2-6.5x+5=0
And then write into (5x-1)(5x-5),why?What's the process between (5x)2-6.5x+5=0 to this equation?

Answer 1

This is not a logarithmic equation. However, to solve it:
52x-(51+50)(.5x)+51=0
= 52x-(101)(.5x)+51
= 52x-(101/2)x+51, since .5 is the same as 1/2
= 52x-50.5x+51
= (52-50.5)x+51
= (1.5)x+51, so the original equation has been reduced to
(1.5)x+51=0
(1.5)x=(-51)
x=(-51)/1.5
=34