How do you find the exact value of $log_5 75-log_5 3$ ?

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Answer 1 · 2017-01-07T05:42:52

$log_5 75 - log_5 3 = 2$

Remember that $log_a b - log_a c = log_a (b/c)$

$:. log_5 75 - log_5 3 = log_5 (75/3) = log_5 25$

Let $x = log_5 25$

$:. 5^x = 25$

$-> 5^x = 5^2$

Equating indices:

$x=2$

Hence: $log_5 75 - log_5 3 = 2$

How do you find the exact value of log_5 75-log_5 3log_5 75-log_5 3?