Question

14c find the domain of the following equations and solve them

Answer 1

`\log _6(x^(-2)+2)=1`
`\log _6((1)/(x^2)^{}+2)=1`

first the domain of the equation is

The domain would be all the real numbers except 0

now, the solution of the equation is:

`\frac{\ln((1)/(x^2)^{}+2)}{\ln6}=1`
`\ln ((1)/(x^2)^{}+2)=\ln 6`
`(1)/(x^2)+2=6^{}`
`(1)/(x^2)=4`
`x^2=(1)/(4)`
`x=\sqrt[]{(1)/(4)}=\pm(1)/(2)`