`4ln(-x)+3=21` Solve the equation. Check for extraneous solutions.

We are asked to solve the following equation:

`4ln(-x)+3=21`

Use basic algebraic rules to isolate the term with the logarithm:

`4ln(-x)=18`

`ln(-x)=9/2`

Exponentiate both sides with base e:

`e^(ln(-x))=e^(9/2)`

`-x=e^(9/2)`

`x=-e^(9/2)~~-90.017`

Substituting back into the original equation shows that the solution works.

The graph:

Comments

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