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

Question

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?

Answer 1

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

Answer 2

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

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