The correct option is right-bracket squared 3 squared =x+5
Step-by-step explanation:
The equation is [tex]\log _{3}(x+5)=2[/tex]
Option a: [tex]\log _{3}(x+5)=3^{2}[/tex]
This is not possible because using logarithmic rule, if [tex]\log _{a} b=c[/tex] then [tex]b=a^{c}[/tex]
Hence, option a is not equivalent to [tex]\log _{3}(x+5)=2[/tex]
Option b: [tex]\log _{3}(x+5)=2^{3}[/tex]
This is not possible because using logarithmic rule, if [tex]\log _{a} b=c[/tex] then [tex]b=a^{c}[/tex]
Hence, option b is not equivalent to [tex]\log _{3}(x+5)=2[/tex]
Option c: [tex]x+5=3^{2}[/tex]
This is possible because using logarithmic rule, if [tex]\log _{a} b=c[/tex] then [tex]b=a^{c}[/tex]
Hence, option c is equivalent to [tex]\log _{3}(x+5)=2[/tex]
Option b: [tex]x+5=2^{3}[/tex]
This is not possible because using logarithmic rule, if [tex]\log _{a} b=c[/tex] then [tex]b=a^{c}[/tex]
Hence, option b is not equivalent to [tex]\log _{3}(x+5)=2[/tex]
Thus, the correct option is c: [tex]x+5=3^{2}[/tex]
Hence, the equation [tex]x+5=3^{2}[/tex] is equivalent to [tex]\log _{3}(x+5)=2[/tex]
