Solutions to Problems on Logarithms

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Section A: Evaluating Logarithms (Ln and Log)

1) ln(e) = 1 2) ln(e2) = 2
3) log(10,000) = 4 4) log(50) = 1.69897
5) ln(10) = 2.3026 6) log(e) = 0.43429
7) log(1) = 0 8) log(100) = 2
9) ln(e6) = 6 10) log(2000) = 3.3010

 

Section B: Logarithms of Fractions

 

1) log(200) - log(2) = 2 2) log(50) + log(20) = 3
3) ln(1/e) = -1 4) log(15/8) = 0.273001
5) ln(e/10) = -1.302585 6) log(100/4) = 1.39794
7) log(1007) = 14 8) log(82/8) = 1.01072

Section C: Algebra of Logarithms

 

1) log(x) = 3       x=3 2) ln(x) = 1       x=e
3) x log(100) = 16       x=8 4) ln(ex) = 7       x=7
5) x log(x) = 10       x=10 6) log(1000) - log(x) = 2       x=10

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