Question

помогите срооочнооо люди умоляю


1. log0,5log381=


2. log4sin6=

3. log183+log186=

4. log5250−log52=

5. log√21024=

6. 491+log72=

7. log216−log864=

8. log3log28−8log82=

9. (log715+log74−log76)∙log107=

Answer 1

$1.log_{0,5}log_{3}81=log_{0,5}(log_{3}81)=log_{0,5}4=-2$

Так как (0,5)⁻²=4

$2. log_{4}sin30 ^{0} = log_{4} frac{1}{2}=-2 \ \ 3. log_{18}3+log_{18}6=log_{18}(3cdot 6)=log_{18}18=1 \ \ 4. log_{5}250-log_{5}2=log_{5} frac{250}{2}=log_{5}125=3$

$5. log_{ sqrt{2} }1024=log_{ sqrt{2}}2^{10}=log_{ sqrt{2} }( sqrt{2})^{20}=20 \ \ 6. 49^{1+log_{7}2}=49^1cdot 49^{log_{7}2}=49^1cdot (7^2)^{log_{7}2}=49^1cdot 7^{2log_{7}2}= \ \ =49^1cdot 7^{log_{7}2^2}=49cdot 2^2=196 \ \ 7. log_{2}16−log_{8}64=4-2=2 \ \ 8. log_{3}log_{2}8-8log_{8}2=log_{3}3- frac{8}{3}log_{8}2^3=1- frac{8}{3}=- frac{5}{3}$

$9. (log_{7}15+log_{7}4-log_{7}6)cdot log_{10}7= log_{7} frac{15cdot 4}{6}cdot log_{10}7= \ \ ==log_{7}10cdot log_{10}7= 1$