Given ${log}_{b} 2 = 0.3562$ $log_b 2= 0.3562$ , ${log}_{b} 3 = 0.5646$ $log_b 3=0.5646$ , and ${log}_{b} 5 = 0.8271$ $log_b 5=0.8271$ , how do you evaluate ${log}_{b} (\frac{5}{3})$ $log_b(5/3)$ ?

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Answer 1 · 2016-05-28T14:41:27

$0.2625$ $0.2625$

Use ${log}_{b} (\frac{m}{n}) = {log}_{b} m - {log}_{b} n$ $log_b (m/n) =log_b m-log_b n$

Here, ${log}_{b} (\frac{5}{3}) = {log}_{b} 5 - {log}_{b} 3 = 0.8271 - 0.5646 = 0.2635$ $log_b(5/3)=log_b 5-log_b 3=0.8271-0.5646=0.2635$ .

Given logb2=0.3562log_b 2= 0.3562, logb3=0.5646log_b 3=0.5646, and logb5=0.8271log_b 5=0.8271, how do you evaluate logb(53)log_b(5/3)?