Question

If $x+{\log }_{10}(1+2^x)=x({\log }_{10}5+{\log }_{10}6)$, then the value of $x$ is

• A. $1$
• B. $0$
• C. $-11$
• D. $-1$

Answer 1

The correct option is A $1$

$x+{\log }_{10}(1+2^x)=x({\log }_{10}5+{\log }_{10}6)=x{\log }_{10}30$

$x+{\log }_{10}(1+2^x)=x(1+{\log }_{10}3)$

$x+{\log }_{10}(1+2^x)=x+x{\log }_{10}3$

$1+2^x=3^x$

$x=1$