Solve the equation. Write the solution set with the exact solutions. Also give approximate solutions to 4
decimal places if necessary.
-$$\log _ { 7 } | x + 5 | = \log _ { 7 } 4$$
A) $\{ - 1 , - 9 \}$
B) $\{ 1 \}$
C) $\{ - 1 \}$
D) $\{ 1,9 \}$

Question

Quizplus · Accepted Answer

Since the bases of the logarithms are the same, the arguments must be equal, leading to $|x + 5| = 4$. Solving this absolute value equation gives $x + 5 = 4$ and $x + 5 = -4$, leading to $x = -1$ and $x = -9$, respectively.

Solve the Equation log⁡7∣x+5∣=log⁡74\log _ { 7 } | x + 5 | = \log _ { 7 } 4log7​∣x+5∣=log7​4

Solve the Equation $\log _ { 7 } | x + 5 | = \log _ { 7 } 4$