161. $2^{x}+2^{x-1}-2^{x-3}=44$.

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161. $2^{x}+2^{x-1}-2^{x-3}=44$.
Solution. Since the smallest exponent is $x-3$, we factor out $2^{x-3}$:

$$
2^{x-3} \cdot\left(2^{3}+2^{2}-1\right)=44 ; 2^{x-3}(8+4-1)=44 ; 2^{x-3} \cdot 11=44
$$

Dividing both sides of the equation by 11, we get

$$
2^{x-3}=4 ; 2^{x-3}=2^{2} ; x-3=2 ; x=5
$$