Open Question: How can I change a logarithm of base 10 to base 5?
20:12 Publicado por Flechado16
First note the change of base formula (let plain "log mean log base 10):
log512 = log 12/log 5
Also note 12 = 4•3 = 2²•3, so log 12 = log 2²•3 = 2•log 2 + log 3 = 2a + b
Further note that 5 = 10/2, so log 5 = log (10/2) = log 10 – log 2 = 1 – log 2 = 1 – a
Thus substituting from the above, log512 = log 12/log 5 = (2a + b)/(1–a)
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