Question

Solve the logarithmic equation. Express all solutions in exact form. $$log_2(x^2 - 49) - log_2(x + 7) = 1$$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { }. (Type an exact solution, using radicals as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.

Name: solve the logarithmic equation express all solutions in exact form log2x2 49 log2x 7 1 select the correct choice below and if necessary fill in the answer box to complete your choice a the 77512
Uploaded: 2024-08-05T06:15:45-08:00
Duration: 1 min 24 s
Channel: Daniel Carr
Description: solve the logarithmic equation express all solutions in exact form log2x2 49 log2x 7 1 select the correct choice below and if necessary fill in the answer box to complete your choice a the 77512

          Solve the logarithmic equation. Express all solutions in exact form.
$$log_2(x^2 - 49) - log_2(x + 7) = 1$$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is { }.
(Type an exact solution, using radicals as needed. Use a comma to separate answers as needed.)
B. The solution is the empty set.

solve the logarithmic equation express all solutions in exact form log2x2 49 log2x 7 1 select the correct choice below and if necessary fill in the answer box to complete your choice a the 77512

Added by Lindsay B.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Daniel Carr

08/05/2024

Step 1

For $log_2(x^2 - 49)$ to be defined, we must have $x^2 - 49 > 0$. This means $(x - 7)(x + 7) > 0$. So, $x < -7$ or $x > 7$. For $log_2(x + 7)$ to be defined, we must have $x + 7 > 0$. This means $x > -7$. Combining these conditions, the domain of the equation is Show more…

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Solve the logarithmic equation. Express all solutions in exact form. $$log_2(x^2 - 49) - log_2(x + 7) = 1$$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { }. (Type an exact solution, using radicals as needed. Use a comma to separate answers as needed.) B. The solution is the empty set.