Question

Помогите решить, пожалуйста, задания по алгебре.
1)1+log8 64
2)19^log12 5
3)3^log3 2+1
4)log12 (49)-log12 (43)
5)log3 6+log9 36-2log3 2
6)log4 (516)-log4 (5)
7)lg20 + lg5

Answer 1

$1)1+log_8 64=1+log_88^2=1+2=3$

$2)log_{ frac{1}{3}} frac{4}{9}-log_{ frac{1}{3}} frac{4}{3}=log_{ frac{1}{3}} frac{4}{9}: frac{4}{3}= log_{ frac{1}{3}} frac{4*3}{9*4}=log_{ frac{1}{3}} frac{1}{3}=1$

$3) log_36+log_936-2log_32= log_36+log_{3^{ frac{1}{2}}} 36-log_32^2= \ \ = log_3(6*36^{ frac{1}{2}} :2^2})=log_3(6*6:4)=log_39=log_33^2=2$

$4)log_4 frac{5}{16}-log_45=log_4 frac{5}{16}:5=log_4 frac{1}{16}=log_44^{-2}=-2$

$5)lg20+lg5=lg(20*5)=lg100=lg10^2=2$


$6) frac{1}{9}^{lg_{ frac{1}{3}}5}= frac{1}{3}^{2lg_{ frac{1}{3}}5}= frac{1}{3}^{lg_{ frac{1}{3}}5^2}=5^2=25$

$3^{log_32+1}= 3^{log_32}*3=2*3=6$