Solve for x: log10(x + 2 ) + log10(x-2) + log103 + 3 log104 - Maths - Indices and Logarithms

Question

Solve for x:

log10(x + 2 ) + log10(x-2) +
log103 + 3 log104

Neha Sethi · Accepted Answer

To find the value of  x put log10(x+2 ) + log10(x-2) + log103 + 3 log104 =0⇒log10x+2x-2=- log103+3 log104      ⇒log10x2-4=-log103+log1043⇒log10x2-4=-log103+log1064⇒log10x2-4=-log10192⇒log10x2-4=log10192-1⇒log10x2-4=log101192logbfx=logbgx⇒fx=gx⇒x2-4=1192⇒x2=769192⇒x=2
0013  approxNote:logab+logac=logabcalogcb=logcbaLog is defined only for positive values