The value of [tex]\log_5{125}[/tex] is 3.
Solution:
Step 1: Given expression is [tex]log_5{125}[/tex].
125 can be expressed as [tex]5^3.[/tex]
[tex]\log_5{125}=\log_5{5}^3[/tex]
Step 2: Using log rule: [tex]\log_a{x^b}=b\log_a{x}[/tex]
[tex]\log_5{5}^3=3\log_5{5}[/tex]
Step 3: Using log rule: [tex]\log_a{a}=1[/tex]
[tex]\log_5{5}= 1[/tex]
⇒ [tex]3\log_5{5}= 3(1)[/tex]
⇒ [tex]3\log_5{5}= 3[/tex]
∴ [tex]\log_5{125}=3[/tex]
Hence the value of [tex]\log_5{125}[/tex] is 3.
