Question

Questões sobre logaritmos:
(novamente)

Answer 1

Bom dia 

1)

a) log2(16) = log2(2^4) = 4log2(2) = 4
b) log4(16) = log4(4^2) = 2log4(4) = 2
c) log3(81) = log3(3^4) = 4log3(3) = 4
d) log5(125) = log5(5^3) = 3log5(5) = 3
e) log(100000) = log10(10^5) = 5log10(10) = 5
f) log8(64) = log8(8^2) = 2log8(8) = 2
g) log2(32) = log2(2^5) = 5log2(2) = 5
h) log6(216) = log6(6^3) = 3log6(6) = 3

2)

a) log2(1/4) = -2log(2)/log(2) = -2
b) log3(√3) = log3(3)/2 = 1/2
c) log8(16) = log(2^4)/log(2^3) = 4/3
d) log4(128) = log(2^7)/log(2^2) = 7/2
e) log36(√2) = log(2)/4log(6)
f) log(0.01) = log(1/100) = -2
g) log9(1/27) = -log(3^3)/log(3^2) = -3/2
h) log0.2(³√25) = log1/5(³√5^2) = -2/3log(5)/log(5) = -2/3
i) log1.25(0.64) = log5/4(64/100) = -log5/4((5/4)^2) = -2
j) log5/3(0.6) = log5/3(3/5) = -1

3)

A = log25(0.2) = log25(1/5) = -0.5
B = log7(49) = log(7^2)/log(7) = 2
C = log25(√8) = 0.323
D = log(0.1) = -1

em ordem crescente D, A, C, B

5) log5(5) + log3(1) - log(10) = 1 + 0 - 1 = 0

b) log1/4(4) + log4(1/4) = -1 -1 = -2
c) log(1000) + log(100) + log(10) + log(1) = 3 + 2 + 1 + 0 = 6
d) 3^log3(2) + 2^log2(3) = 2 + 3 = 5
e) log8(log3(9)) = log8(2) = 1/3
f) log9(log4(64)) + log4(log3(81)) = log9(3) + log4(4) = 1/2 + 1 = 3/2