How do you calculate $log_3 sqrt243$ ?

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Answer 1 · 2016-04-24T01:38:25

First, use the exponent rule $root(a)(n) = n^(1/a)$

$log_3(243^(1/2))$

Now, use the log rule $loga^n = nloga$

$1/2log_3(243)$

Now, use the log rule $log_an = logn/loga$

$1/2(log243/log3)$

Rewrite 243 in base 3.

$1/2((log3^5)/log3)$

$1/2((5log3)/log3)$

$1/2 xx 5$

$5/2$

Thus, completely simplified, $log_3(sqrt(243)) = 5/2 or 2.5$

Hopefully this helps!

How do you calculate log_3 sqrt243 log_3 sqrt243?