+0  
 
0
56
1
avatar+204 

Real numbers a and b satisfy the equations $3^a=81^{b+2}$ and $125^b=5^{a-3}$. What is ab?

 Feb 24, 2021
 #1
avatar+939 
+1

Rewrite:

 

\(3^a = 3^{4(b+2)}\)

 

\(5^{3b} = 5^{a-3}\)

 

Get rid of the exponents:

 

a = 4(b + 2)

3b = a - 3

 

Then you can solve.

 Feb 24, 2021

66 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar