Question

Answer the following:

Show that, `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|` = 0

Answer 1

L.H.S. = `log |sqrt(x^2 + 1) + x | + log | sqrt(x^2 + 1) - x|`

= `log |(sqrt(x^2 + 1) + x) (sqrt(x^2 + 1) - x)|`

= log |x² + 1 – x²|

= log 1

= 0

= R.H.S.