Question

Solve for the variable in the equation below.Round to the nearest hundredth.Do not round any intermediate computations.e^x=9 5^(y+4)= 4

Answer 1

Given the following equations

$\begin{gathered} e^x=9 \\ 5^{(y+4)}=4 \end{gathered}$

For the first equation

$\begin{gathered} e^x=9 \\ intdroduce\text{ logarithm to both sides} \\ lne^x=ln9 \\ xlne=ln9 \\ x=ln9 \\ x=2.1972 \\ x\approx2.20 \end{gathered}$

For the second equation

$\begin{gathered} 5^{(y+4)}=4 \\ Introduce\text{ logarithm to both sides} \\ ln5^{(y+4)}=ln4 \\ (y+4)ln5=ln4 \\ y+4=\frac{ln4}{ln5} \\ y+4=0.8614 \end{gathered}$$\begin{gathered} y=0.8614-4 \\ y=-3.1386 \\ y\approx-3.14 \end{gathered}$

Hence, the value of x is approximately 2.20 and the value of y is approximately -3.14