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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

 Dec 4, 2021
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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 \(b, \) \(\boxed{x=a+2b+1}\)


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