Question

encontre o valor dos logaritmos :

A)log10 100
B)log 1/4 16
C)log9 1
D)log 2/5 28/4

Answer 1

a) log 10 100
2 × log 10 10
2 × 1
2

b) log1/4 16
1/4^x = 4^2
4^-1x = 4^2
-x = 2
x = -2

c) log 9 1
9^x = 1
9^x = 9^0
x = 0

d)

Answer 2

Olá!

$a) log_{10}(100) \\ {10}^{x} = 100 \\ {10}^{x} = {10}^{2} \\ x = 2 \\ \\ b) \: log_{ \frac{1}{4} }(16) \\ \frac{1}{4}^{x} = 16 \\ \frac{1}{4}^{x} = {2}^{4} \\ \frac{1}{2^{2} }^{x} = {2}^{4} \\ \frac{1}{2}^{2x} = {2}^{4} \\ \frac{1}{2}^{2x} = \frac{1}{2}^{ - 4} \\ 2x = - 4 \\ x = \frac{ - 4}{2} \\ x = - 2 \\ \\ c) \: log_{9}(1) \\ {9}^{x} = 1 \\ {9}^{x} = {9}^{0} \\ x = 0$

d) log 2/5 (28/4)

Usando as propriedades...

log 2/5 (28/4) = x
log 2/5 (7) = x
2/5^x = 7
x = - 2,12 ( aproximados )

Espero ter ajudado. Bons estudos!!