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# hard

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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

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 $$b,$$ $$\boxed{x=a+2b+1}$$