Real numbers a and b satisfy the equations $3^a=81^{b+2}$ and $125^b=5^{a-3}$. What is ab?
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.
+205 
+1224 
