Pregunta
Solve the following logarithmic equation.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is { }.
(Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.
B. There is no solution.
A. The solution set is { }.
(Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.
B. There is no solution.
Ask by Wright Craig. in the United States
Dec 16,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The solution set is { -1 }.
Solución

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Como
Extra Insights
Let’s solve the equation step by step!
We can combine the logarithms using the property that
.
So, we rewrite the equation as:
This implies:
Now, expand the left-hand side:
Setting the equation:
Now, simplify:
Next, we can factor this quadratic:
Setting each factor to zero gives us:
So,
or
.
However, we must ensure these solutions don’t create logarithms of negative numbers. We check the individual solutions:
For
:
For
:
Thus, the only solution is
. Therefore, the correct choice is:
A. The solution set is {-1}.
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