Question

Se log x = 3 + log 3 − log 2 – 2 . log 5 , então x é igual a:

Answer 1

Estou enferrujado em log, mas vamos ver se acerto ...

$\log x = 3 + (log3 -log2) - 2* log5$



$\log x + 2 \log5 = ( \log3-\log2)+3$

$\log x +\log 5^2 = \log (3/2) +3$

$\log25x=\log(3/2) +3$

$\log( \frac{25x}{ \frac{3}{2}}})=3$

$\log( \frac{50x}{3})=3$

$10^3 = \frac{50x}{3}$

$1000= \frac{50x}{3}$

$3000=50x$

$\frac{3000}{50} =x$

x = 60

Answer 2

$log_{x} a + log_{x} b <=> log_{x} (a*b)$
$log_{x} a - log_{x} b <=> log_{x} (a/b)$
$log_{x}(a^{n}) = n * log_{x}a$
_____________________________

$logx = 3 + (log3 - log2) - 2*log5$
$logx = 3 + log3 - log2 - log5^{2}$
$logx = log10^{3} + log3 - log2 - log25$
$logx = log(10^{3}*3 / [2*25])$
$logx = log(3000/50)$
$logx = log60$
$x = 60$