+0  
 
0
97
1
avatar

If \(3^x = 27^{y - 5}\) and \(2^y = 8^{2x - 4}\), then find y - x.

 May 31, 2020
 #1
avatar+30940 
+1

Note that \(27=3^3 \text{ and } 8=2^3\)

 

So  \(3^x = 3^{3(y-5)} \text{ and }2^y=2^{3(2x-4)}\)

 

Now equate powers so that you have two equations for x and y:

 

x = 3(y - 5)   and   y = 3(2x - 4)

 

Can you take it from here?

 Jun 1, 2020

13 Online Users