Question

Solve for $x:$
$x+{\log }_{10}(1+2^x)=x.{\log }_{10}5+{\log }_{10}6$

• A. $1$
• B. $2$
• C. $3$
• D. None of these

Answer 1

The correct option is A $1$

Let $\left(2^x\right)=u$

$\therefore u^2+u-6=0$

$(u+3)(u-2)=0$

$u=-3$ or $u=2$

$u=-3\left(\alpha \right)$

$\therefore u=2$

$2^x=2$

$\therefore x=1$