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

1 Answer
Jake M.
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.](http://www.wolframalpha.com/input/?i=y%20=%202%5E%28-x-3%29;%20y%20=%203%5E%28x%2b1%29)

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.

Related questions
See all questions in Exponential and Logistic Functions on a Graphing Calculator
Impact of this question
2485 views around the world
You can reuse this answer
Creative Commons License