Answer:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
Step-by-step explanation:
Given
[tex]log_3(\frac{21}{5})[/tex]
Required
Express in terms of [tex]log_3(5)[/tex] and [tex]log_3(7)[/tex]
[tex]log_3(\frac{21}{5})[/tex]
Express 21 as 7 * 3
[tex]log_3(\frac{21}{5}) = log_3(\frac{7 * 3}{5})[/tex]
Apply law of logarithm
[tex]log_3(\frac{21}{5}) = log_3(7) + log_3(3) - log_3(5)[/tex]
[tex]log_3(3) = 1[/tex]. So, we have:
[tex]log_3(\frac{21}{5}) = log_3(7) + 1 - log_3(5)[/tex]
Rewrite:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
