Question

Using properties of logarithms in excersises 13-18, use the properties of logarithms o write the logarithm in terms of log3(5) and log3(7) log3 (21/5)

Answer 1

Answer:

$log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1$

Step-by-step explanation:

Given

$log_3(\frac{21}{5})$

Required

Express in terms of $log_3(5)$ and $log_3(7)$

$log_3(\frac{21}{5})$

Express 21 as 7 * 3

$log_3(\frac{21}{5}) = log_3(\frac{7 * 3}{5})$

Apply law of logarithm

$log_3(\frac{21}{5}) = log_3(7) + log_3(3) - log_3(5)$

$log_3(3) = 1$. So, we have:

$log_3(\frac{21}{5}) = log_3(7) + 1 - log_3(5)$

Rewrite:

$log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1$