`ln(x+19)=ln(7x-8)` Solve the equation. Check for extraneous solutions.

Expert Answers

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To evaluate the equation `ln(x+19)=ln(7x-8)` , we apply natural logarithm property: `e^(ln(x))=x` .

Raise both sides by base of `e` .



Subtract `7x` from both sides of the equation.



Subtract 19 from both sides of the equation.



Divide both sides by `-6` .



Checking: Plug-in `x=9/2` on `ln(x+19)=ln(7x-8)` .



`ln(47/2)=ln(47/2) `      TRUE

Thus, the `x=9/2` is the real exact solution of the equation `ln(x+19)=ln(7x-8)` .  There is no extraneous solution.

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