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

$\begin{gathered} \log_44^{(x+3)}=\log_47 \\ \\ (x+3)\operatorname{\log}_44=\operatorname{\log}_47 \\ \\ (x+3)=\log_47 \\ \\ x=\log_47-3 \\ \end{gathered}$

Apply change of base

we have that

$\log_47=\frac{log7}{log4}$

substitute

$\begin{gathered} x=\frac{log7}{log4}-3 \\ \\ x=-1.596 \end{gathered}$