Take it easy

$7(2^x) = 112\Rightarrow x = log_2 (\frac{112}{7}) = 4$

$2^x + 2^x + 2^x + 2^{x+2} = 112$

Factorizing $2^x + 2^x + 2^x + 2^{x+2}$

$2^x + 2^x + 2^x + 2^{x+2}$

$2^x + 2^0 \cdot 2^x + 2^0 \cdot 2^x + 2^2 \cdot 2^x$

$= 2^x(1+2^0+2^0+2^2)$

$= 7 \cdot 2^x$

Now,

$7 \cdot 2^x =112$

$2^x = 16$

Convert 16 to base 2.

$2^x = 2^4$ $~ ~ ~ ~ ~~ ~ ~$ $;16 = 2^4$

$x = \boxed{4}$

$2^x+2^x+2^x+2^{x+2}=112$

$3(2^x)+2^x(2^2)=112$

$2^x(3+4)=112$

$2^x(7)=112$

$2^x=\dfrac{112}{7}$

$2^x=16$

$2^x=2^4$

$\color{#D61F06}\boxed{x=4}$