log5√7x−4−12=log5√x+2
log5√7x−4−log5√x+2=12
log5(√7x−4√x+2)=12 [∵loga(MN)=logaM−logaN]
log5(7x−4x+2)12=12
12[log5(7x−4x+2)]=12 [∵logaMn=nlogaM]
log5(7x−4x+2)=1
51=7x−4x+2 (exponential form)
Cross multiplying, 7x−4=5(x+2)
7x−4=5x+10⟹7x−5x=10+4
⟹2x=14
∴x=7