math - Difference between 12Log2 and Log[2,12]? -

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my math pretty weak, , i'm having confusion on differences. i'm trying find out midi formula, output frequency when have midi value

midinumber = 69+12* log2(440/frequency)

so derived frequency = (-69 + 5280 log2 + midinumber)/(12 log2)

if plugin things works correctly 440 = (-69 + 5280 log2 + 69)/(12 log2)

if though things not work correctly (-69 + log[2, 5280.] + 69)/log[2, 12.]

this output in programming, don't know difference between 2 equations. maybe it's 12*log2, 12*log2[1] or, ...? no idea.

part of confusion seems treating log2(n) log2 * n. log2 function, inverse of 2^x.

so derivation should go follows:

midinumber = 69 + 12 * log2(440 / frequency) midinumber - 69 = 12 * log2(440 / frequency) (midinumber - 69) / 12 = log2(440 / frequency) 2^((midinumber - 69) / 12) = 440 / frequency frequency = 440 / 2^((midinumber - 69) / 12)

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