Suppose that 3^a = 2 and 3^b = 5. If 3^x = 150,then write an expression for x in terms of a and b
+483 By the law of exponents, if \(3^a=2, \) and \(3^b=5,\) then \(3^{a+2b}=2 \cdot 5 \cdot 5 = 50.\) Now we know that \(50 \cdot 3 = 150, \) so \(3^{a+2b+1}=150,\) so in terms of \(a\) and \(b, \) \(\boxed{x=a+2b+1}\)
