Answer:
The correct option is right-bracket squared 3 squared =x+5
Step-by-step explanation:
The equation is \log _{3}(x+5)=2
Option a: \log _{3}(x+5)=3^{2}
This is not possible because using logarithmic rule, if \log _{a} b=c then b=a^{c}
Hence, option a is not equivalent to \log _{3}(x+5)=2
Option b: \log _{3}(x+5)=2^{3}
This is not possible because using logarithmic rule, if \log _{a} b=c then b=a^{c}
Hence, option b is not equivalent to \log _{3}(x+5)=2
Option c: x+5=3^{2}
This is possible because using logarithmic rule, if \log _{a} b=c then b=a^{c}
Hence, option c is equivalent to \log _{3}(x+5)=2
Option b: x+5=2^{3}
This is not possible because using logarithmic rule, if \log _{a} b=c then b=a^{c}
Hence, option b is not equivalent to \log _{3}(x+5)=2
Thus, the correct option is c: x+5=3^{2}
Hence, the equation x+5=3^{2} is equivalent to \log _{3}(x+5)=2
→ 3 ≠ 1 → A is eliminated.
→ 5 ≠
→ B is eliminated.
→ 2 = 2 → C satisfies the equation.
→ 10 ≠
→ D is eliminated.
→ -1 = -1 → E satisfies the equation.
→ 3 = 3 → F satisfies the equation.