Question

How do you use the graphing calculator to solve `2^(-x-3)=3^(x+1)`?

Answer 1

`x approx -1.774...`

Explanation:

We can plot both functions on the same plot and see where they intersect.

Socratic doesn't have a good way to plot two functions as far as I know, so you can see a good plot here.

We could also do this analytically using logarithms:
`ln(2^(-x-3)) = ln(3^(x+1))`
`ln(2)(-x-3) = ln(3)(x+1)`
`ln(3)(x+1) + ln(2)(x+3) = 0`
`ln(6)x + ln(24) = 0`
`x = - (ln(24))/(ln(6)) = -log_6(24) approx -1.774...`

which is exactly where we saw it in the above.