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=(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