Question

if log1000^x =-1/4 then x is​

Answer 1

$Answer \: \\ \\ Given \: \: Question \: \: Is \: \: \\ \\ log(1000 {}^{x} ) = \frac{ - 1}{4} \\ \\ x log(1000) = \frac{ - 1}{4} \\ \\ x log(10 {}^{3} ) = \frac{ - 1}{4} \\ \\ 3x log(10) = \frac{ - 1}{4} \\ \\ 3x = \frac{ - 1}{4} \\ \\ x = \frac{ - 1}{12} \\ \\ Note \: \\ \\ 1) \: \: \: log(x {}^{n} ) = n log(x) \\ \\ 2) \ \: \: log(10) = 1$

Answer 2

Answer:

→ $x = \frac{ - 1}{12}$

Step-by-step explanation:

$\begin{lgathered}\\ \\ log(1000 {}^{x} ) = \frac{ - 1}{4} \\ \\ x log(1000) = \frac{ - 1}{4} \\ \\ x log(10 {}^{3} ) = \frac{ - 1}{4} \\ \\ 3x log(10) = \frac{ - 1}{4} \\ \\ 3x = \frac{ - 1}{4} \\ \\ x = \frac{ - 1}{12} \\ \\ \end{lgathered}$