Question

Explain how solve 4^(x+3)=7 using the change of base formula: (imaged below). Include the solution for x in your answer and round to the nearest thousandth

Answer 1

we have the equation

`4^((x+3))=7`

Solve for x

Apply log of base 4 on both sides

so

Apply change of base

we have that

`\log_47=(log7)/(log4)`

substitute

`\begin{gathered} x=(log7)/(log4)-3 \\ \\ x=-1.596 \end{gathered}`