Question

Suppose log8(3)=a and log8(5)=b. What is log 8(45) in terms of a and b?

Answer 1

Answer: 2a+b

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Work Shown:

`\log_8(3) = a\\\\\log_8(5) = b\\\\\log_8(45) = \log_8(3*3*5)\\\\\log_8(45) = \log_8(3)+\log_8(3)+\log_8(5)\\\\\log_8(45) = a+a+b\\\\\log_8(45) = 2a+b\\\\`

The log rule used was log(x*y) = log(x)+log(y).