Number system — Question 7

0.01x = 2

Take logarithm on both sides,

$x\log \frac{1}{100}=\log 2$

x log 10–2 = log 2

–2x log 10 = log 2

–2x = log 2 (log 10 = 1)

$x=\frac{-\log 2}{2}$