Question

вычислите log5 625 log7 343 log3 729 log0.5 0.125 log1.2 1.44 log3/4 81/256 log3 1/27 log1/6 36 log1/9 729 log1/8 512

Answer 1

$log_5 525=log_5 5^4=4*log_5 5=4*1=4;$

 

$log_7 343=log_7 7^3=3*log_7 7=3*1=3;$

 

$log_{0.5} 0.125=log_{0.5} 0.5^3=3*log_{0.5} 0.5=3*1=3;$

 

$log_{1.2} 1.44=log_{1.2} 1.2^2=2*log_{1.2} 1.2=2*1=2;$

 

$log_{frac{3}{4}} frac{81}{256}=log_{frac{3}{4}} (frac{3}{4})^4=4*log_{frac{3}{4}} frac{3}{4}=4*1=4;$

 

$log_3 frac{1}{27}=log_3 3^{-3}=-3*log_3 3=-3*1=-3;$

 

$log_{frac{1}{6}} frac{1}{36}=log_{frac{1}{6}} (frac{1}{6})^2=2*log_{frac{1}{6}} frac{1}{6}=2*1=2;$

 

$log_{frac{1}{9}} 729=log_{frac{1}{9}} (frac{1}{9})^{-3}=-3;$

 

$log_{frac{1}{8}} 512=log_{frac{1}{8}} (frac{1}{8})^{-3}=-3$