How do you evaluate $3 {log}_{3} (9) - 4 {log}_{3} (3)$ $3 log_3 (9) - 4 log_3 (3)$ ?

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Answer 1 · 2016-05-19T02:04:52

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Use ${log}_{b} a = \frac{log a}{log b}, n log a = {log a}^{n} and {log}_{b} b = 1$ $log _b a = log a/log b, n log a = log a^n and log_b b=1$ .

Here, $3 {log}_{3} 9 - 4 {log}_{3} 3$ $3 log_3 9 - 4 log_3 3$

$= 3 (\frac{log 9}{log 3}) - 4 (1)$ $=3(log 9/log 3)-4(1)$

$= 3 (\frac{log (3^{2})}{log 3}) - 4$ $=3(log (3^2)/log 3)-4$

$= 6 (\frac{log 3}{log 3}) - 4 = 6 - 4 = 2$ $=6(log 3/log 3)-4=6-4 = 2$

How do you evaluate 3log3(9)−4log3(3)3 log_3 (9) - 4 log_3 (3)?