If x = (100)^a, y = (10000)^b and z = (10)^c, express log 10√y/x^2 z^3 in terms of a, b, c.

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Prove the following:
log₁₀4 ÷ log₁₀2 = log₃9

Prove the following:
log₁₀25+ log₁₀4 = log₅25