Given: Log2=a, Log7=b. Find: Log 56.

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I don't know how to solve this. Can someone help me? How do I use the information above to help me find Log 56?

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2 Answers

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$\log(56) = \log(7\cdot8) = \log(7) + \log(8) = \log(7) + \log\left(2^{3}\right) = \log(7) + 3\log(2) = b + 3a$

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Hint 1: $56= 7\cdot 2^3$

Hint 2: $\log (x\cdot y^z)= \log x+ z\log y$

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