Mathematic Problems
xlog10x+53=105+log10x
xlog10x+53=105+log10xlog1010
x13log10x+5=105+log10x1
x13log10x+5=105+log10x   log10()
log10x13·log10x+5=log10105+log10x
13·log10x+5·log10x=5+log10x·log1010
13·log10x+5·log10x=5+log10x·1
log10x=t
13·t+5·t=5+t
t+5·t=15+3t 
t2+5t=15+3t 
t2+5t-15-3t=0 
t2+2t-15=0 
t1,2=-2±22-4·1·-152
t1,2=-2±4+602=-2±642
t1,2=-2±82
t1,2=-1±4
t1=3 ; t2=-5
log10x1=3
x1=103=1000
log10x2=-5
x2=10-5=1105
x103,10-5
x103,10-5