How do you evaluate $log_3 (1/81)$ ?

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Answer 1 · 2016-10-18T17:32:05

By reducing the logarithm using the laws of logs, and reducing the number to a power of the base the result follows. $=-4$

$color(red)(log_"3"(1/81)=log_"3"(1)-log_"3"81)$

since

$log_a(X/Y)=log_a(X)-log_a(Y)$

$color(red)(log_"3"(1/81)=0-log_"3"3^4)$

since $log_a1=0$

$AAa inRR$

$color(red)(log_"3"(1/81)=-4log_"3"3)$

since $log_aX^n=nlog_aX$

$color(red)(log_"3"(1/81)=-4)$

since $log_aa=1$

How do you evaluate log_3 (1/81)log_3 (1/81)?