Question

If $\log 3=0.477$ and $(1000{)}^x=3$, then the value of $x$ will be

• A. $0.159$
• B. $0.62$
• C. $0.162$
• D. $0.59$

Answer 1

The correct option is A $0.159$

Since, $(1000{)}^x=3$
$\therefore \log \left[\right(1000{)}^x]=\log 3$
$\Rightarrow x\log 1000=\log 3$
$\Rightarrow x\log \left({10}^3\right)=\log 3$
$\Rightarrow x\cdot 3\log 10=\log 3$

$\Rightarrow 3x=\frac{\log 3}{\log 10}$

$\Rightarrow x=\frac{0.477}{3\times 1}=0.159$