To solve this logarithmic equation, we first need to rewrite it in exponential form.
The given equation is:
[tex] log_{x}(x^{2} - 2x + 6) = 2 [/tex]
This can be rewritten as:
[tex] x^{2} - 2x + 6 = x^{2} [/tex]
Subtracting [tex] x^{2} [/tex] from both sides gives:
[tex] -2x + 6 = 0 [/tex]
Solving for x by moving 6 to the other side gives:
[tex] -2x = -6 [/tex]
Dividing by -2 gives:
[tex] x = 3 [/tex]
Therefore, the solution to the equation is [tex] x = 3 [/tex].
To solve this logarithmic equation, we first need to rewrite it in exponential form.
The given equation is:
[tex] log_{x}(x^{2} - 2x + 6) = 2 [/tex]
This can be rewritten as:
[tex] x^{2} - 2x + 6 = x^{2} [/tex]
Subtracting [tex] x^{2} [/tex] from both sides gives:
[tex] -2x + 6 = 0 [/tex]
Solving for x by moving 6 to the other side gives:
[tex] -2x = -6 [/tex]
Dividing by -2 gives:
[tex] x = 3 [/tex]
Therefore, the solution to the equation is [tex] x = 3 [/tex].