Question

If ${\log }_7(2x^2-1)=2$, then the value of $x$ is equal to

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is A $5$

${\log }_7(2x^2-1)=2$

$\therefore \frac{\log (2x^2-1)}{\log 7}=2$ ....(${\log }_{b}a=\frac{\log a}{\log b}$)

$\therefore \log (2x^2-1)=2\log 7$

$\therefore \log (2x^2-1)=\log 7^2$ ....($\log a^b=b\log a$)

$\therefore (2x^2-1)=7^2$

$\therefore 2x^2-50=0$

$\therefore x^2-25=0$

$\therefore x=\pm 5$