Question

a3
4) Se log(a) = 4 e log(b) = 1, então log
é igual:
b
1
a)
11
b)
3
c) V3.
d) 3.
e) 5.​

Answer 1

Resposta:

$log(a) = 4 = > a = {10}^{4} = > a = 10 \: 000 \\ log(b) = 1 = > b = {10}^{1} = > b = 10$

$log_{a}(b) = log_{ {10}^{4} }(10) = x \\ ({10}^{4} ) {}^{x} = 10 \\ {10}^{4x} = 10 \\ 4x = 1 \\ x = \frac{1}{4}$

$log( \frac{b}{1} ) = log(b) = log(10) = {10}^{x} = 10 = > x = 1$

$log(a) = log(10 {}^{4} ) = x \\ 4 \times log(10) = x \\ 4 \times 1 = 4$

$log(a) - log(b) = \\ 4 - 1 = 3$