Using the change of base property of logarithms, it is found that the expression that correctly shows [tex]\log_{11}{5}[/tex] rewritten using a log of base 8 is:
[tex]\log_{11}{5} = \frac{\log_8{5}}{\log_8{11}}[/tex]
To change the base of a logarithm from a to c, we use the following rule:
[tex]\log_{a}{b} = \frac{\log_c{a}}{\log_c{b}}[/tex]
Hence, in this question, the coefficients are [tex]a = 11, b = 5, c = 8[/tex], and the equivalent expression is:
[tex]\log_{11}{5} = \frac{\log_8{5}}{\log_8{11}}[/tex]
A similar problem is given at https://brainly.com/question/13594713
