Question

Determine X de modo que log10 (1000)×-log10 (0,001)×=1.


(Obs:Log (1000)elevado a x na base 10
Log (0,001) elevado a x na base 10)

Answer 1

$log 1000^{x} - log (0,001)^{x} = 1 \\ \\ log (10^{3})^{x} - log (10^{-3})^{x}=1 \\ \\ log 10^{3x}- log 10^{-3x} = 1 \\ \\ log \frac{10{3x}}{10^{-3x}}=1 \\ \\ log 10^{3x - (-3x)} = 1 \\ \\ log 10^{6x} = 1 \\ \\ 10^{1}=10^{6x} \\ \\ 6x = 1 \\ \\ x = \frac{1}{6}$

Espero ter ajudado.