Question

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

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

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

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