Question

Q.40. Solve the following equations :
(i) $3\left(2^x+1\right)-2^{x+2}+5=0$

Answer 1

$$\begin{gathered} 3\left(2^{\mathrm{x}}+1\right)-2^{\mathrm{x}+2}+5=0 \\ \Rightarrow 3.2^{\mathrm{x}}+3-2^{\mathrm{x}}.2^2+5=0 \\ \Rightarrow 3.2^{\mathrm{x}}-4.2^{\mathrm{x}}+8=0 \\ \Rightarrow 3\mathrm{y}-4\mathrm{y}+8=0\left[\mathbf{Take}\mathbf{}{\mathbf{2}}^{\mathbf{x}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{y}\right] \\ \Rightarrow \mathrm{y}=8 \\ \Rightarrow 2^{\mathrm{x}}=2^3 \\ \Rightarrow \mathrm{x}=3 \end{gathered}$$