1.

Solve for x : log(x-1) + log(x+1) = log 1 a base 2

Answer» USING property,

log(x) + log(y) = log(xy)

LHS=

log((x - 1)(x + 1)) \\ = log( {x}^{2} - 1)

and RHS =
log_{2}(1) = log(1)

Equating LHS and RHS,
{x}^{2} - 1 = 1 \\ {x}^{2} = 2 \\ x = + \sqrt{2}

IGNORING the negative value SINCE the argument TAKES only positive ones.


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