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

1 Answer
Apr 29, 2018

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.