For a,c0, a,c 1 and b0: log_a b= log_c blog_c a Examples log_9 x= log_3 xlog_3 9= 12log_3 x (x0)

Question

For a,c>0, a,c 1 and b>0: log_a b= log_c blog_c a Examples log_9 x= log_3 xlog_3 9= 12log_3 x (x>0) log_5 18= lg18lg5= ln18ln5 1.80 (3 s.f.) Reciprocal identity log_a b= 1log_b a (b 1) log_x 3= [[fill]] 1log_3 x[[/fill]] (x>0, x 1)

Accepted Answer

$\log_a b=\dfrac{\log_c b}{\log_c a}$

Change of Base and Its Proof

Change of Base and Its Proof

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