Question

A rectangular tank is 25 m long and 9.5 m deep. If 600 cubic meters of water be drawn off the tank, the level of water in the tank goes down by 1.5 m.

Calculate the width of the tank.

Answer 1

${\log }_{10}250=\log (10\times 25)={\log }_{10}10+{\log }_{10}25=1+{\log }_{10}25$.....................$({\log }_{10}10=1)$

$2{\log }_{10}x+1=1+{\log }_{10}25$

i.e. $2{\log }_{10}x={\log }_{10}25$

But $2\log x=\log x^2$.....................(Power law)

${\log }_{10}{x}^2={\log }_{10}25$

$x^2=25$

i.e. $x=5$

$\therefore {\log }_{10}2x={\log }_{10}10=1$