Question

Rezolva ecuatiile va rooooog

Answer 1

$\displaystyle \mathtt{a)lgx+lg \sqrt{x} =3 \Rightarrow lgx+lgx^{ \frac{1}{2} }=3 \Rightarrow lgx+ \frac{1}{2}lgx=3\Rightarrow }\\ \\ \mathtt{\Rightarrow 2lgx+lgx=6 \Rightarrow 3lgx=6 \Rightarrow lgx= \frac{6}{3} \Rightarrow lgx=2 \Rightarrow x=10^2 \Rightarrow } \\ \\ \mathtt{\Rightarrow }\mathbf{x=100}$

$\displaystyle \mathtt{b)2^x+2^{x+3}=36 \Rightarrow 2^x+2^x \cdot 2^3=36 \Rightarrow 2^x(1+8)=36 \Rightarrow } \\ \\ \mathtt{\Rightarrow 2^x \cdot 9=36 \Rightarrow 2^x=4 \Rightarrow 2^x=2^2 \Rightarrow }\mathbf{x=2}$