Question

alguem consegue responde essas questoes ??
estou em recuperaçao e preciso da ajuda de voces !! obrigado !!

usando as definiçoes ,calcule
a) log 3/ 27
b) log 10 000
c) log 1/2 32
d) log 2/ √¯8
e) log 1/4 16
f ) log 2/3 8/27
g ) log 2/ 0,25
h ) log 7/ 7
i ) log 4/ 1

Answer 1

$a)log_{3} 27=x \\ 3 ^{x}=27 \\ 3 ^{x} =3 ^{3} \\ x=3 \\ \\ b)log10000=x \\ 10 ^{x} =10000 \\ 10 ^{x}=10 ^{4} \\ x=4 \\ \\ c)log _{ \frac{1}{2} } 32=x \\ (\frac{1}{2}) ^{x}=32 \\ (2^{-1} ) ^{x}= 2 ^{5} \\ 2 ^{-x}=2 ^{5} \\ -x=5*(-1) \\ x=-5$

$d)log _{2} \sqrt{8} =x \\ 2 ^{x}=8 ^{ \frac{1}{2} } \\ 2^{x}=(2 ^{3}) ^{ \frac{1}{2} } \\ 2 ^{x}=2 ^{ \frac{3}{2} } \\ x= \frac{3}{2} \\ \\ e)log _{ \frac{1}{4} } 16=x \\ (\frac{1}{4}) ^{x} =16 \\ (\frac{1}{4}) ^{x} =4 ^{2} \\ 4 ^{-x} =4 ^{2} \\ -x=2*(-1) \\ x=-2$

$f)log _{ \frac{2}{3} } \frac{8}{27} =x \\ ( \frac{2}{3}) ^{x}= \frac{8}{27} \\ ( \frac{2}{3}) ^{x}= (\frac{2}{3}) ^{3} \\ x=3 \\ \\ g)log _{2}0,25=x \\ 2 ^{x}= \frac{25}{100} \\ \\ 2 ^{x}=( \frac{5}{10}) ^{2} \\ \\ 2 ^{x}=( \frac{1}{2}) ^{2} \\ 2 ^{x}=(2 ^{-1} ) ^{2} \\ 2 ^{x}=2^{-2} \\ x=-2$

$h)Log _{7}7=x \\ 7 ^{x}=7 \\ x=1 \\ \\ i)log _{4}1=x \\ 4 ^{x} =1 \\ x=0$