IainR308533 IainR308533
  • 25-10-2022
  • Mathematics
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14c find the domain of the following equations and solve them

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

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SamsonM660282 SamsonM660282
  • 25-10-2022
[tex]\log _6(x^{-2}+2)=1[/tex][tex]\log _6(\frac{1}{x^2}^{}+2)=1[/tex]

first the domain of the equation is

The domain would be all the real numbers except 0

now, the solution of the equation is:

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

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