Expressions can be represented as logarithms and exponents
Rogelio argument is correct
<h3>How to determine if Rogelio's claim is true</h3>
The logarithmic equation is given as:
![\log_5(15635)](https://tex.z-dn.net/?f=%5Clog_5%2815635%29)
Apply logarithm rule, to rewrite the logarithmic equation
![\log_5(15635) = \frac{\log(15635)}{\log(5)}](https://tex.z-dn.net/?f=%5Clog_5%2815635%29%20%3D%20%5Cfrac%7B%5Clog%2815635%29%7D%7B%5Clog%285%29%7D)
Evaluate the individual logarithmic expressions
![\log_5(15635) = \frac{4.1941}{0.6990}](https://tex.z-dn.net/?f=%5Clog_5%2815635%29%20%3D%20%5Cfrac%7B4.1941%7D%7B0.6990%7D)
Evaluate the quotient (i.e. divide the expression)
![\log_5(15635) = 6.0001](https://tex.z-dn.net/?f=%5Clog_5%2815635%29%20%3D%206.0001)
The above equation shows that
is between 6 and 7
Hence, Rogelio argument is correct
Read more about equivalent expressions at:
brainly.com/question/2972832