Question

Помогите вычислить (задание с логарифмами)☻☺

Answer 1

1)
$8(log_{2} \sqrt{48} -log_{4}3+log_{16} \frac{1}{128} )= \\ \\ =8(log_{2}4 \sqrt{3} -log_{2^2}3+log_{2^4}2^{-7})= \\ \\ =8(log_{2}4 \sqrt{3}- \frac{1}{2}log_{2}3+ \frac{1}{4}*(-7)log_{2}2 )= \\ \\ =8(log_{2}4 \sqrt{3}-log_{2} \sqrt{3}- \frac{7}{4} )=$
$=8(log_{2} \frac{4 \sqrt{3} }{ \sqrt{3} }- \frac{7}{4} )=8(log_{2}4- \frac{7}{4} )= \\ \\ =8(2- \frac{7}{4} )=8*2-8* \frac{7}{4} =16-14=2$
Ответ: 2

2)
$0.25*(1+9^{log_{3}5})^{log_{26}8}=0.25*(1+3^{2log_{3}5})^{log_{26}8}= \\ \\ =0.25*(1+3^{log_{3}5^2})^{log_{26}8}=0.25*(1+5^2)^{log_{26}8}= \\ \\ =0.25*(1+25)^{log_{26}8}=0.25*26^{log_{26}8}=0.25*8=2$
Ответ: 2.