Question

Solve for x if log(x - 1) + log(x + 1) = log21​

Answer 1

sqrt(22) =
`√(22)`

Explanation:

we can use the logarithm rule, "log x + log y = log(xy)" to solve this problem

log(x-1) + log(x+1) = =
`log((x-1)(x+1))` = log(21)

this means that x^2 - 1 equals 21

xx-1 = 21

xx=22

x=sqrt(22)

Answer 2

Answer:
`x=\pm √(22)`

Explanation:

`\log(x-1)+\log(x+1)=\log 21\\\\\log((x-1)(x+1))=\log 21\\\\\log(x^2-1)=\log 21\\\\x^2-1=21\\\\x^2=22\\\\x=\pm √(22)`