Question

If $1+2{\log }_{10}x={\log }_{10}250$, then the value of $x$ is equal to

Answer 1

Since base is given 10 ,.

${\log }_{10}250={\log }_{10}(10\times 25)={\log }_{10}10+{\log }_{10}25=1+\log 25$ [Using $({\log }_{10}10=1)$]

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

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

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

$\therefore {\log }_{10}{x}^2={\log }_{10}{5}^2$

$\therefore x^2=25$

$\therefore x=5$