Question

solve log (x – 21) = 2 – log x

Answer 1

log (x - 21) + log x = 2
log [x (x - 21)] = 2
x (x - 21) = 100
x^2 - 21x - 100 = 0
Solve the equation, reject any answers for which x ≤ 21

Answer 2

\[log(x-21)=2-logx\]
\[log(x-21)+logx=2\]
\[log{(x-21)(x)}=2\]
\[10^{log{(x-21)(x)}}=10^2\]
\[(x-21)(x)=100\]
\[x^2-21x=100\]
\[x^2-21x-100=0\]
\[x^2-25x+4x-100=0\]
\[x(x-25)+4(x-25)=0\]
\[(x+4)(x-25)=0\]
\[x=-4 , x=25\]

Answer 3

\[x = \frac{-(-21)±\sqrt{21^2-4(1)(-100)}}{2(1)}\]
\[x = \frac{21±\sqrt{841}}{2}\]
\[x = \frac{21±29}{2}\]
\[x = 25 OR x=-4(NA)\]