Question

Given a^2=b^2+1, prove that loga+b X=-loga-b X

Answer 1

given a^2=b^2+1
or a^2-b^2=1
or (a+b)(a-b) =1

taking log of both sides (same base)
log (a+b)(a-b) = log 1
or log(a+b) +log(a-b) =0 [as log 1=0 ]
or log(a+b) = - log(a-b)

Answer 2

Thank you ,I'm grateful^^