Question

How do you solve `400(1-0.2)^x=50`?

Answer 1

`x=ln(8)/ln(5/4)`

Explanation:

`400(1-0.2)^x=50`
`ln(400(1-0.2)^x)=ln50`
`lnab=lna+lnb`
`ln400+ln(0.8^x)=ln50`
`lna^b=blna`
`ln400+xln0.8=ln50`
`xln0.8=ln(50/400)`
`xln0.8=ln(1/8)`
`cancel(-)xln(5/4)=cancel(-)ln8`
`x=ln(8)/ln(5/4)`
\0/ here's our answer!