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MathNet 2016-part-04 — 184 problems (EN–VI) Question 30

Math Olympiad Vault · MathNet 2016-part-04 — 184 problems (EN–VI)

Question 30

a) Show that the number $\log_{2015} 2016$ is irrational;

b) Compare the numbers $\log_{5} 6$ and $\log_{6} 7$;

c) Compute $E=\lg^{3} 5+\lg^{3} 20+\lg 8 \cdot \lg (0,25)$.