Question

Решите логарифмы. Три номера
$1) frac{ lg27+lg3}{lg15-lg5} ...2) lg30 + lg20 - lg6 ...3) 0,01^{log_{10}3-1 }$

Answer 1

$mathtt{frac{lg27+lg3}{lg15-lg5}=frac{lg(27*3)}{lg(15:5)}=frac{lg81}{lg3}=log_381=4}$

$mathtt{lg30+lg20-lg6=lg(frac{30*20}{6})=lg(5*20)=lg100=2}$

$mathtt{0,01^{lg3-1}=(10^{-2})^{lg3-1}=10^{2-2lg3}=10^2*(10^{lg9})^{-1}=frac{100}{9}}$