How do you simplify $log_5 (17/8) log_5 (51/16)$ ?

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Answer 1 · 2017-02-04T07:15:59

$log_5(17/8)log_5(51/16)=1.18862$

$log_5(17/8)log_5(51/16)$

= $log_5(17/8xx51/16)$

= $log_5((17xx17xx3)/(8xx8xx2))$

= $2log_5(17/8)+log_5(3/2)$ as $loga^nb=nloga+logb$

Now as $log_5u=logu/log5$ , this can be written as

$(2log(17/8)+log(3/2))/log5$

= $(2log(2.125)+log(1.5))/log5$

= $(2xx0.32736+0.17609)/(0.69897)$

= $1.18862$

How do you simplify log_5 (17/8) log_5 (51/16)log_5 (17/8) log_5 (51/16)?