Question

Given loga (m) = 10 and loga (n) = 25 , find loga (m * n ^ 2)

Answer 1

The result of the log function $log_a (m * n ^ 2)$  is 60

According to the law of logarithm if $log_ab=y$ then $b=a^y$

Given the following expressions

$log_am=10\\log_an=25$

This can be expressed as

$m =a^{10} \ and \ n = a^{25}$

Substitute the value of m and n into the expression $log_a (m * n ^ 2)$ to have:

$log_a (m * n ^ 2) = log_a(a^{10}\times a^{50})\\=log_aa^{60}\\=60log_aa\\=60(1) \\= 60$

This shows that the result of the log function $log_a (m * n ^ 2)$  is 60

Learn more here: brainly.com/question/12049968