{2}^(x + 2 ) = 9 *( {2}^(x) ) - 2 pls how is this solved​

Question

`{2}^(x + 2 ) = 9 *( {2}^(x) ) - 2`
pls how is this solved​

Answer 1

Hello, please consider the following.

`{2}^(x + 2 ) = 9 *( {2}^(x) ) - 2\\\\2^x \cdot 2^2=9\cdot 2^x-2\\\\(9-4)2^x = 2\\\\2^x=(2)/(5)\\\\\text{We take the ln.}\\\\xln(2)=ln(2)-ln(5)\\\\x=(ln(2)-ln(5))/(ln(2))=-1.32193...`

Let me know if you need further explanation.

Thank you