`log_6(3x-10)=log_6(14-5x)` Solve the equation. Check for extraneous solutions.

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To evaluate the equation `log_6(3x-10)=log_6(14-5x)` , we apply logarithm property: `a^(log_a(x))=x` .

Raised both sides by base of `6` .



Add `10` on both sides.



Add `5x ` on both sides.



Divide both sides by `8` .



Checking: Plug-in `x=3` on `log_6(3x-10)=log_6(14-5x)` .



`log_3(-1)=?log_3(-1) FALSE`

A logarithm `log_b(x)` is undefined for `xlt=0` .

Thus, the `x=3` is an extraneous solution of the given equation `log_6(3x-10)=log_6(14-5x)` . There is no real solution.


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